title: Newton's laws of motion

text: If the body is not released from rest but instead launched upwards and/or horizontally with nonzero velocity, then free fall becomes projectile motion. When air resistance can be neglected, projectiles follow parabola-shaped trajectories, because gravity affects the body's vertical motion and not its horizontal. At the peak of the projectile's trajectory, its vertical velocity is zero, but its acceleration is formula_50 downwards, as it is at all times. Setting the wrong vector equal to zero is a common confusion among physics students.


title: Newton's laws of motion

text: When a body is in uniform circular motion, the force on it changes the direction of its motion but not its speed. For a body moving in a circle of radius formula_43 at a constant speed formula_54, its acceleration has a magnitudeformula_55and is directed toward the center of the circle. The force required to sustain this acceleration, called the centripetal force, is therefore also directed toward the center of the circle and has magnitude formula_56. Many orbits, such as that of the Moon around the Earth, can be approximated by uniform circular motion. In such cases, the centripetal force is gravity, and by Newton's law of universal gravitation has magnitude formula_57, where formula_41 is the mass of the larger body being orbited. Therefore, the mass of a body can be calculated from observations of another body orbiting around it.


title: Newton's laws of motion

text: Newton's cannonball is a thought experiment that interpolates between projectile motion and uniform circular motion. A cannonball that is lobbed weakly off the edge of a tall cliff will hit the ground in the same amount of time as if it were dropped from rest, because the force of gravity only affects the cannonball's momentum in the downward direction, and its effect is not diminished by horizontal movement. If the cannonball is launched with a greater initial horizontal velocity, then it will travel farther before it hits the ground, but it will still hit the ground in the same amount of time. However, if the cannonball is launched with an even larger initial velocity, then the curvature of the Earth becomes significant: the ground itself will curve away from the falling cannonball. A very fast cannonball will fall away from the inertial straight-line trajectory at the same rate that the Earth curves away beneath it; in other words, it will be in orbit (imagining that it is not slowed by air resistance or obstacles).


title: Newton's laws of motion

text: Consider a body of mass formula_27 able to move along the formula_60 axis, and suppose an equilibrium point exists at the position formula_61. That is, at formula_61, the net force upon the body is the zero vector, and by Newton's second law, the body will not accelerate. If the force upon the body is proportional to the displacement from the equilibrium point, and directed to the equilibrium point, then the body will perform simple harmonic motion. Writing the force as formula_63, Newton's second law becomes


title: Newton's laws of motion

text: where the frequency formula_66 is equal to formula_67, and the constants formula_68 and formula_69 can be calculated knowing, for example, the position and velocity the body has at a given time, like formula_70.


title: Newton's laws of motion

text: One reason that the harmonic oscillator is a conceptually important example is that it is good approximation for many systems near a stable mechanical equilibrium. For example, a pendulum has a stable equilibrium in the vertical position: if motionless there, it will remain there, and if pushed slightly, it will swing back and forth. Neglecting air resistance and friction in the pivot, the force upon the pendulum is gravity, and Newton's second law becomes formula_71where formula_13 is the length of the pendulum and formula_73 is its angle from the vertical. When the angle formula_73 is small, the sine of formula_73 is nearly equal to formula_73 (see Taylor series), and so this expression simplifies to the equation for a simple harmonic oscillator with frequency formula_77.


title: Newton's laws of motion

text: A harmonic oscillator can be "damped," often by friction or viscous drag, in which case energy bleeds out of the oscillator and the amplitude of the oscillations decreases over time. Also, a harmonic oscillator can be "driven" by an applied force, which can lead to the phenomenon of resonance.


title: Newton's laws of motion

text: Newtonian physics treats matter as being neither created nor destroyed, though it may be rearranged. It can be the case that an object of interest gains or loses mass because matter is added to or removed from it. In such a situation, Newton's laws can be applied to the individual pieces of matter, keeping track of which pieces belong to the object of interest over time. For instance, if a rocket of mass formula_78, moving at velocity formula_79, ejects matter at a velocity formula_80 relative to the rocket, then


title: Newton's laws of motion

text: A rigid body is an object whose size is too large to neglect and which maintains the same shape over time. In Newtonian mechanics, the motion of a rigid body is often understood by separating it into movement of the body's center of mass and movement around the center of mass.


title: Newton's laws of motion

text: Significant aspects of the motion of an extended body can be understood by imagining the mass of that body concentrated to a single point, known as the center of mass. The location of a body's center of mass depends upon how that body's material is distributed. For a collection of pointlike objects with masses formula_83 at positions formula_84, the center of mass is located at formula_85 where formula_41 is the total mass of the collection. In the absence of a net external force, the center of mass moves at a constant speed in a straight line. This applies, for example, to a collision between two bodies. If the total external force is not zero, then the center of mass changes velocity as though it were a point body of mass formula_41. This follows from the fact that the internal forces within the collection, the forces that the objects exert upon each other, occur in balanced pairs by Newton's third law. In a system of two bodies with one much more massive than the other, the center of mass will approximately coincide with the location of the more massive body.


title: Newton's laws of motion

text: When Newton's laws are applied to rotating extended bodies, they lead to new quantities that are analogous to those invoked in the original laws. The analogue of mass is the moment of inertia, the counterpart of momentum is angular momentum, and the counterpart of force is torque.


title: Newton's laws of motion

text: Angular momentum is calculated with respect to a reference point. If the displacement vector from a reference point to a body is formula_88 and the body has momentum formula_34, then the body's angular momentum with respect to that point is, using the vector cross product, formula_90 Taking the time derivative of the angular momentum gives formula_91 The first term vanishes because formula_92 and formula_93 point in the same direction. The remaining term is the torque, formula_94 When the torque is zero, the angular momentum is constant, just as when the force is zero, the momentum is constant. The torque can vanish even when the force is non-zero, if the body is located at the reference point (formula_95) or if the force formula_30 and the displacement vector formula_88 are directed along the same line.


title: Newton's laws of motion

text: The angular momentum of a collection of point masses, and thus of an extended body, is found by adding the contributions from each of the points. This provides a means to characterize a body's rotation about an axis, by adding up the angular momenta of its individual pieces. The result depends on the chosen axis, the shape of the body, and the rate of rotation.


title: Newton's laws of motion

text: Newton's law of universal gravitation states that any body attracts any other body along the straight line connecting them. The size of the attracting force is proportional to the product of their masses, and inversely proportional to the square of the distance between them. Finding the shape of the orbits that an inverse-square force law will produce is known as the Kepler problem. The Kepler problem can be solved in multiple ways, including by demonstrating that the Laplace–Runge–Lenz vector is constant, or by applying a duality transformation to a 2-dimensional harmonic oscillator. However it is solved, the result is that orbits will be conic sections, that is, ellipses (including circles), parabolas, or hyperbolas. The eccentricity of the orbit, and thus the type of conic section, is determined by the energy and the angular momentum of the orbiting body. Planets do not have sufficient energy to escape the Sun, and so their orbits are ellipses, to a good approximation; because the planets pull on one another, actual orbits are not exactly conic sections.


title: Newton's laws of motion

text: If a third mass is added, the Kepler problem becomes the three-body problem, which in general has no exact solution in closed form. That is, there is no way to start from the differential equations implied by Newton's laws and, after a finite sequence of standard mathematical operations, obtain equations that express the three bodies' motions over time. Numerical methods can be applied to obtain useful, albeit approximate, results for the three-body problem. The positions and velocities of the bodies can be stored in variables within a computer's memory; Newton's laws are used to calculate how the velocities will change over a short interval of time, and knowing the velocities, the changes of position over that time interval can be computed. This process is looped to calculate, approximately, the bodies' trajectories. Generally speaking, the shorter the time interval, the more accurate the approximation.


title: Newton's laws of motion

text: Newton's laws of motion allow the possibility of chaos. That is, qualitatively speaking, physical systems obeying Newton's laws can exhibit sensitive dependence upon their initial conditions: a slight change of the position or velocity of one part of a system can lead to the whole system behaving in a radically different way within a short time. Noteworthy examples include the three-body problem, the double pendulum, dynamical billiards, and the Fermi–Pasta–Ulam–Tsingou problem.


title: Newton's laws of motion

text: Newton's laws can be applied to fluids by considering a fluid as composed of infinitesimal pieces, each exerting forces upon neighboring pieces. The Euler momentum equation is an expression of Newton's second law adapted to fluid dynamics. A fluid is described by a velocity field, i.e., a function formula_98 that assigns a velocity vector to each point in space and time. A small object being carried along by the fluid flow can change velocity for two reasons: first, because the velocity field at its position is changing over time, and second, because it moves to a new location where the velocity field has a different value. Consequently, when Newton's second law is applied to an infinitesimal portion of fluid, the acceleration formula_99 has two terms, a combination known as a "total" or "material" derivative. The mass of an infinitesimal portion depends upon the fluid density, and there is a net force upon it if the fluid pressure varies from one side of it to another. Accordingly, formula_100 becomes


title: Newton's laws of motion

text: where formula_102 is the density, formula_103 is the pressure, and formula_104 stands for an external influence like a gravitational pull. Incorporating the effect of viscosity turns the Euler equation into a Navier–Stokes equation:


title: Newton's laws of motion

text: It is mathematically possible for a collection of point masses, moving in accord with Newton's laws, to launch some of themselves away so forcefully that they fly off to infinity in a finite time. This unphysical behavior, known as a "noncollision singularity", depends upon the masses being pointlike and able to approach one another arbitrarily closely, as well as the lack of a relativistic speed limit in Newtonian physics.


title: Newton's laws of motion

text: It is not yet known whether or not the Euler and Navier–Stokes equations exhibit the analogous behavior of initially smooth solutions "blowing up" in finite time. The question of existence and smoothness of Navier–Stokes solutions is one of the Millennium Prize Problems.


title: Newton's laws of motion

text: Classical mechanics can be mathematically formulated in multiple different ways, other than the "Newtonian" description (which itself, of course, incorporates contributions from others both before and after Newton). The physical content of these different formulations is the same as the Newtonian, but they provide different insights and facilitate different types of calculations. For example, Lagrangian mechanics helps make apparent the connection between symmetries and conservation laws, and it is useful when calculating the motion of constrained bodies, like a mass restricted to move along a curving track or on the surface of a sphere. Hamiltonian mechanics is convenient for statistical physics, leads to further insight about symmetry, and can be developed into sophisticated techniques for perturbation theory. Due to the breadth of these topics, the discussion here will be confined to concise treatments of how they reformulate Newton's laws of motion.


title: Newton's laws of motion

text: Lagrangian mechanics differs from the Newtonian formulation by considering entire trajectories at once rather than predicting a body's motion at a single instant. It is traditional in Lagrangian mechanics to denote position with formula_107 and velocity with formula_108. The simplest example is a massive point particle, the Lagrangian for which can be written as the difference between its kinetic and potential energies:


title: Newton's laws of motion

text: and the potential energy is some function of the position, formula_111. The physical path that the particle will take between an initial point formula_112 and a final point formula_113 is the path for which the integral of the Lagrangian is "stationary". That is, the physical path has the property that small perturbations of it will, to a first approximation, not change the integral of the Lagrangian. Calculus of variations provides the mathematical tools for finding this path. Applying the calculus of variations to the task of finding the path yields the Euler–Lagrange equation for the particle,


title: Newton's laws of motion

text: which is a restatement of Newton's second law. The left-hand side is the time derivative of the momentum, and the right-hand side is the force, represented in terms of the potential energy.


title: Newton's laws of motion

text: Landau and Lifshitz argue that the Lagrangian formulation makes the conceptual content of classical mechanics more clear than starting with Newton's laws. Lagrangian mechanics provides a convenient framework in which to prove Noether's theorem, which relates symmetries and conservation laws. The conservation of momentum can be derived by applying Noether's theorem to a Lagrangian for a multi-particle system, and so, Newton's third law is a theorem rather than an assumption.


title: Newton's laws of motion

text: In Hamiltonian mechanics, the dynamics of a system are represented by a function called the Hamiltonian, which in many cases of interest is equal to the total energy of the system. The Hamiltonian is a function of the positions and the momenta of all the bodies making up the system, and it may also depend explicitly upon time. The time derivatives of the position and momentum variables are given by partial derivatives of the Hamiltonian, via Hamilton's equations. The simplest example is a point mass formula_27 constrained to move in a straight line, under the effect of a potential. Writing formula_107 for the position coordinate and formula_118 for the body's momentum, the Hamiltonian is


title: Newton's laws of motion

text: which reproduces the familiar statement that a body's momentum is the product of its mass and velocity. The time derivative of the momentum is


title: Newton's laws of motion

text: which, upon identifying the negative derivative of the potential with the force, is just Newton's second law once again.


title: Newton's laws of motion

text: As in the Lagrangian formulation, in Hamiltonian mechanics the conservation of momentum can be derived using Noether's theorem, making Newton's third law an idea that is deduced rather than assumed.


title: Newton's laws of motion

text: Among the proposals to reform the standard introductory-physics curriculum is one that teaches the concept of energy before that of force, essentially "introductory Hamiltonian mechanics".


title: Newton's laws of motion

text: The Hamilton–Jacobi equation provides yet another formulation of classical mechanics, one which makes it mathematically analogous to wave optics. This formulation also uses Hamiltonian functions, but in a different way than the formulation described above. The paths taken by bodies or collections of bodies are deduced from a function formula_124 of positions formula_125 and time formula_126. The Hamiltonian is incorporated into the Hamilton–Jacobi equation, a differential equation for formula_127. Bodies move over time in such a way that their trajectories are perpendicular to the surfaces of constant formula_127, analogously to how a light ray propagates in the direction perpendicular to its wavefront. This is simplest to express for the case of a single point mass, in which formula_127 is a function formula_130, and the point mass moves in the direction along which formula_127 changes most steeply. In other words, the momentum of the point mass is the gradient of formula_127:


title: Newton's laws of motion

text: The relation to Newton's laws can be seen by considering a point mass moving in a time-independent potential formula_135, in which case the Hamilton–Jacobi equation becomes


title: Newton's laws of motion

text: Interchanging the order of the partial derivatives on the left-hand side, and using the power and chain rules on the first term on the right-hand side,


title: Newton's laws of motion

text: This is another re-expression of Newton's second law. The expression in brackets is a "total" or "material" derivative as mentioned above, in which the first term indicates how the function being differentiated changes over time at a fixed location, and the second term captures how a moving particle will see different values of that function as it travels from place to place:


title: Newton's laws of motion

text: In statistical physics, the kinetic theory of gases applies Newton's laws of motion to large numbers (typically on the order of Avogadro's number) of particles. Kinetic theory can explain, for example, the pressure that a gas exerts upon the container holding it as the aggregate of many impacts of atoms, each imparting a tiny amount of momentum.


title: Newton's laws of motion

text: The Langevin equation is a special case of Newton's second law, adapted for the case of describing a small object bombarded stochastically by even smaller ones. It can be writtenformula_142where formula_143 is a drag coefficient and formula_144 is a force that varies randomly from instant to instant, representing the net effect of collisions with the surrounding particles. This is used to model Brownian motion.


title: Newton's laws of motion

text: Newton's three laws can be applied to phenomena involving electricity and magnetism, though subtleties and caveats exist.


title: Newton's laws of motion

text: Coulomb's law for the electric force between two stationary, electrically charged bodies has much the same mathematical form as Newton's law of universal gravitation: the force is proportional to the product of the charges, inversely proportional to the square of the distance between them, and directed along the straight line between them. The Coulomb force that a charge formula_145 exerts upon a charge formula_146 is equal in magnitude to the force that formula_146 exerts upon formula_145, and it points in the exact opposite direction. Coulomb's law is thus consistent with Newton's third law.


title: Newton's laws of motion

text: Electromagnetism treats forces as produced by "fields" acting upon charges. The Lorentz force law provides an expression for the force upon a charged body that can be plugged into Newton's second law in order to calculate its acceleration. According to the Lorentz force law, a charged body in an electric field experiences a force in the direction of that field, a force proportional to its charge formula_107 and to the strength of the electric field. In addition, a "moving" charged body in a magnetic field experiences a force that is also proportional to its charge, in a direction perpendicular to both the field and the body's direction of motion. Using the vector cross product,formula_150


title: Newton's laws of motion

text: If the electric field vanishes (formula_151), then the force will be perpendicular to the charge's motion, just as in the case of uniform circular motion studied above, and the charge will circle (or more generally move in a helix) around the magnetic field lines at the cyclotron frequency formula_152. Mass spectrometry works by applying electric and/or magnetic fields to moving charges and measuring the resulting acceleration, which by the Lorentz force law yields the mass-to-charge ratio.


title: Newton's laws of motion

text: Collections of charged bodies do not always obey Newton's third law: there can be a change of one body's momentum without a compensatory change in the momentum of another. The discrepancy is accounted for by momentum carried by the electromagnetic field itself. The momentum per unit volume of the electromagnetic field is proportional to the Poynting vector.


title: Newton's laws of motion

text: There is subtle conceptual conflict between electromagnetism and Newton's first law: Maxwell's theory of electromagnetism predicts that electromagnetic waves will travel through empty space at a constant, definite speed. Thus, some inertial observers seemingly have a privileged status over the others, namely those who measure the speed of light and find it to be the value predicted by the Maxwell equations. In other words, light provides an absolute standard for speed, yet the principle of inertia holds that there should be no such standard. This tension is resolved in the theory of special relativity, which revises the notions of "space" and "time" in such a way that all inertial observers will agree upon the speed of light in vacuum.


title: Newton's laws of motion

text: In special relativity, the rule that Wilczek called "Newton's Zeroth Law" breaks down: the mass of a composite object is not merely the sum of the masses of the individual pieces. Newton's first law, inertial motion, remains true. A form of Newton's second law, that force is the rate of change of momentum, also holds, as does the conservation of momentum. However, the definition of momentum is modified. Among the consequences of this is the fact that the more quickly a body moves, the harder it is to accelerate, and so, no matter how much force is applied, a body cannot be accelerated to the speed of light. Depending on the problem at hand, momentum in special relativity can be represented as a three-dimensional vector, formula_153, where formula_27 is the body's rest mass and formula_143 is the Lorentz factor, which depends upon the body's speed. Alternatively, momentum and force can be represented as four-vectors.


title: Newton's laws of motion

text: Newtonian mechanics is a good approximation to special relativity when the speeds involved are small compared to that of light.


title: Newton's laws of motion

text: General relativity is theory of gravity that advances beyond that of Newton. In general relativity, gravitational force is reimagined as curvature of spacetime. A curved path like an orbit is not the result of a force deflecting a body from an ideal straight-line path, but rather the body's attempt to fall freely through a background that is itself curved by the presence of other masses. A remark by John Archibald Wheeler that has become proverbial among physicists summarizes the theory: "Spacetime tells matter how to move; matter tells spacetime how to curve." Wheeler himself thought of this reciprocal relationship as a modern, generalized form of Newton's third law. The relation between matter distribution and spacetime curvature is given by the Einstein field equations, which require tensor calculus to express.


title: Newton's laws of motion

text: The Newtonian theory of gravity is a good approximation to the predictions of general relativity when gravitational effects are weak and objects are moving slowly compared to the speed of light.


title: Newton's laws of motion

text: Quantum mechanics is a theory of physics originally developed in order to understand microscopic phenomena: behavior at the scale of molecules, atoms or subatomic particles. Generally and loosely speaking, the smaller a system is, the more an adequate mathematical model will require understanding quantum effects. The conceptual underpinning of quantum physics is very different from that of classical physics. Instead of thinking about quantities like position, momentum, and energy as properties that an object "has", one considers what result might "appear" when a measurement of a chosen type is performed. Quantum mechanics allows the physicist to calculate the probability that a chosen measurement will elicit a particular result. The expectation value for a measurement is the average of the possible results it might yield, weighted by their probabilities of occurrence.


title: Newton's laws of motion

text: The Ehrenfest theorem provides a connection between quantum expectation values and Newton's second law, a connection that is necessarily inexact, as quantum physics is fundamentally different from classical. In quantum physics, position and momentum are represented by mathematical entities known as Hermitian operators, and the Born rule is used to calculate the expectation values of a position measurement or a momentum measurement. These expectation values will generally change over time; that is, depending on the time at which (for example) a position measurement is performed, the probabilities for its different possible outcomes will vary. The Ehrenfest theorem says, roughly speaking, that the equations describing how these expectation values change over time have a form reminiscent of Newton's second law. However, the more pronounced quantum effects are in a given situation, the more difficult it is to derive meaningful conclusions from this resemblance.


title: Newton's laws of motion

text: The concepts invoked in Newton's laws of motion — mass, velocity, momentum, force — have predecessors in earlier work, and the content of Newtonian physics was further developed after Newton's time. Newton combined knowledge of celestial motions with the study of events on Earth and showed that one theory of mechanics could encompass both.


title: Newton's laws of motion

text: The subject of physics is often traced back to Aristotle; however, the history of the concepts involved is obscured by multiple factors. An exact correspondence between Aristotelian and modern concepts is not simple to establish: Aristotle did not clearly distinguish what we would call speed and force, and he used the same term for density and viscosity; he conceived of motion as always through a medium, rather than through space. In addition, some concepts often termed "Aristotelian" might better be attributed to his followers and commentators upon him. These commentators found that Aristotelian physics had difficulty explaining projectile motion. Aristotle divided motion into two types: "natural" and "violent". The "natural" motion of terrestrial solid matter was to fall downwards, whereas a "violent" motion could push a body sideways. Moreover, in Aristotelian physics, a "violent" motion requires an immediate cause; separated from the cause of its "violent" motion, a body would revert to its "natural" behavior. Yet a javelin continues moving after it leaves the hand of its thrower. Aristotle concluded that the air around the javelin must be imparted with the ability to move the javelin forward. John Philoponus, a Byzantine Greek thinker active during the sixth century, found this absurd: the same medium, air, was somehow responsible both for sustaining motion and for impeding it. If Aristotle's idea were true, Philoponus said, armies would launch weapons by blowing upon them with bellows. Philoponus argued that setting a body into motion imparted a quality, impetus, that would be contained within the body itself. As long as its impetus was sustained, the body would continue to move. In the following centuries, versions of impetus theory were advanced by individuals including Nur ad-Din al-Bitruji, Avicenna, Abu'l-Barakāt al-Baghdādī, John Buridan, and Albert of Saxony. In retrospect, the idea of impetus can be seen as a forerunner of the modern concept of momentum. (The intuition that objects move according to some kind of impetus persists in many students of introductory physics.)


title: Newton's laws of motion

text: The modern concept of inertia is credited to Galileo. Based on his experiments, Galileo concluded that the "natural" behavior of a moving body was to keep moving, until something else interfered with it. Galileo recognized that in projectile motion, the Earth's gravity affects vertical but not horizontal motion. However, Galileo's idea of inertia was not exactly the one that would be codified into Newton's first law. Galileo thought that a body moving a long distance inertially would follow the curve of the Earth. This idea was corrected by Isaac Beeckman, René Descartes, and Pierre Gassendi, who recognized that inertial motion should be motion in a straight line.


title: Newton's laws of motion

text: Christiaan Huygens, in his "Horologium Oscillatorium" (1673), put forth the hypothesis that "By the action of gravity, whatever its sources, it happens that bodies are moved by a motion composed both of a uniform motion in one direction or another and of a motion downward due to gravity." Newton's second law generalized this hypothesis from gravity to all forces.


title: Newton's laws of motion

text: One important characteristic of Newtonian physics is that forces can act at a distance without requiring physical contact. For example, the Sun and the Earth pull on each other gravitationally, despite being separated by millions of kilometres. This contrasts with the idea, championed by Descartes among others, that the Sun's gravity held planets in orbit by swirling them in a vortex of transparent matter, "aether". Newton considered aetherial explanations of force but ultimately rejected them. The study of magnetism by William Gilbert and others created a precedent for thinking of "immaterial" forces, and unable to find a quantitatively satisfactory explanation of his law of gravity in terms of an aetherial model, Newton eventually declared, "I feign no hypotheses": whether or not a model like Descartes's vortices could be found to underlie the "Principia"'s theories of motion and gravity, the first grounds for judging them must be the successful predictions they made. And indeed, since Newton's time every attempt at such a model has failed.


title: Newton's laws of motion

text: Johannes Kepler suggested that gravitational attractions were reciprocal — that, for example, the Moon pulls on the Earth while the Earth pulls on the Moon — but he did not argue that such pairs are equal and opposite. In his "Principles of Philosophy" (1644), Descartes introduced the idea that during a collision between bodies, a "quantity of motion" remains unchanged. Descartes defined this quantity somewhat imprecisely by adding up the products of the speed and "size" of each body, where "size" for him incorporated both volume and surface area. Moreover, Descartes thought of the universe as a plenum, that is, filled with matter, so all motion required a body to displace a medium as it moved. During the 1650s, Huygens studied collisions between hard spheres and deduced a principle that is now identified as the conservation of momentum. Christopher Wren would later deduce the same rules for elastic collisions that Huygens had, and John Wallis would apply momentum conservation to study inelastic collisions. Newton cited the work of Huygens, Wren, and Wallis to support the validity of his third law.


title: Newton's laws of motion

text: Newton arrived at his set of three laws incrementally. In a 1684 manuscript written to Huygens, he listed four laws: the principle of inertia, the change of motion by force, a statement about relative motion that would today be called Galilean invariance, and the rule that interactions between bodies do not change the motion of their center of mass. In a later manuscript, Newton added a law of action and reaction, while saying that this law and the law regarding the center of mass implied one another. Newton probably settled on the presentation in the "Principia," with three primary laws and then other statements reduced to corollaries, during 1685.


title: Newton's laws of motion

text: Newton expressed his second law by saying that the force on a body is proportional to its change of motion, or momentum. By the time he wrote the "Principia," he had already developed calculus (which he called "the science of fluxions"), but in the "Principia" he made no explicit use of it, perhaps because he believed geometrical arguments in the tradition of Euclid to be more rigorous. Consequently, the "Principia" does not express acceleration as the second derivative of position, and so it does not give the second law as formula_156. This form of the second law was written (for the special case of constant force) at least as early as 1716, by Jakob Hermann; Leonhard Euler would employ it as a basic premise in the 1740s. Euler pioneered the study of rigid bodies and established the basic theory of fluid dynamics. Pierre-Simon Laplace's five-volume "Traité de mécanique céleste" (1798–1825) forsook geometry and developed mechanics purely through algebraic expressions, while resolving questions that the "Principia" had left open, like a full theory of the tides.


title: Newton's laws of motion

text: The concept of energy became a key part of Newtonian mechanics in the post-Newton period. Huygens' solution of the collision of hard spheres showed that in that case, not only is momentum conserved, but kinetic energy is as well (or, rather, a quantity that in retrospect we can identify as one-half the total kinetic energy). The question of what is conserved during all other processes, like inelastic collisions and motion slowed by friction, was not resolved until the 19th century. Debates on this topic overlapped with philosophical disputes between the metaphysical views of Newton and Leibniz, and variants of the term "force" were sometimes used to denote what we would call types of energy. For example, in 1742, Émilie du Châtelet wrote, "Dead force consists of a simple tendency to motion: such is that of a spring ready to relax; living force is that which a body has when it is in actual motion." In modern terminology, "dead force" and "living force" correspond to potential energy and kinetic energy respectively. Conservation of energy was not established as a universal principle until it was understood that the energy of mechanical work can be dissipated into heat. With the concept of energy given a solid grounding, Newton's laws could then be derived within formulations of classical mechanics that put energy first, as in the Lagrangian and Hamiltonian formulations described above.


title: Newton's laws of motion

text: Modern presentations of Newton's laws use the mathematics of vectors, a topic that was not developed until the late 19th and early 20th centuries. Vector algebra, pioneered by Josiah Willard Gibbs and Oliver Heaviside, stemmed from and largely supplanted the earlier system of quaternions invented by William Rowan Hamilton.


title: Michael Oher

text: Michael Jerome Oher (; né Williams Jr.; born May 28, 1986) is a former American football offensive tackle who played in the National Football League (NFL) for eight seasons, primarily with the Baltimore Ravens. He played college football at the University of Mississippi, where he earned unanimous All-American honors, and was selected by the Ravens in the first round of the 2009 NFL Draft. He also played for the Tennessee Titans and Carolina Panthers.


title: Michael Oher

text: Oher's life through his final year of high school and first year of college is one of the subjects of Michael Lewis' 2006 book, "", and was featured in the Academy Award-winning 2009 film "The Blind Side".


title: Michael Oher

text: Born Michael Jerome Williams, Jr., in Memphis, Tennessee, he was one of 12 children of Denise Oher. His mother suffered from alcoholism and crack cocaine addiction, and his father, Michael Jerome Williams, was frequently in prison. He received little attention and discipline during his childhood. He repeated first and second grades, and attended eleven schools during his first nine years as a student. He was placed in foster care at age seven, and alternated between living in various foster homes and periods of homelessness. Oher's father was a former cellmate of Denise Oher's brother and was murdered in prison when Oher was a senior in high school.


title: Michael Oher

text: Oher played football during his freshman year at a public high school in Memphis. He applied for admission to Briarcrest Christian School at the suggestion of Tony Henderson, an auto mechanic with whom he was living temporarily. Henderson was enrolling his son at the school to fulfill the dying wish of the boy's grandmother and thought Oher might enroll as well. The school's football coach, Hugh Freeze, submitted Oher's school application to the headmaster, who agreed to accept him if Oher could complete a home study program first. He did not finish the program, but was admitted when the headmaster realized that his requirement had removed Oher from the public education system.


title: Michael Oher

text: Coached by Freeze and Tim Long, Briarcrest's offensive line coach, Oher was named Division II (2A) Lineman of the Year in 2003, and First-team Tennessee All-State. Scout.com rated Oher a five-star recruit and the No. 5 offensive lineman prospect in the country. Before that season and for his prior 20 months at Briarcrest, Oher had been living with several foster families. In 2004, Leigh Anne and Sean Tuohy, a couple with a daughter and son attending Briarcrest, allowed Oher to live with them and eventually adopted him. The family began tending to his needs after becoming familiar with his difficult childhood. They also hired a tutor for him, who worked with him for 20 hours per week.


title: Michael Oher

text: Oher also earned two letters each in track and basketball. He averaged 22 points and 10 rebounds a game, earning All-State honors by helping lead the basketball team to a 27–6 record, winning the district championship as a senior. Oher was also a state runner-up in the discus as a senior.


title: Michael Oher

text: Oher's low grades were initially a barrier to his acceptance to an NCAA program. He eventually increased his 0.76 grade point average (GPA) to a 2.52 GPA by the end of his senior year so he could attend a Division I school by enrolling in some 10-day-long Internet-based courses from Brigham Young University. Taking and passing the internet courses allowed him to replace Ds and Fs earned in earlier school classes, such as English, with As earned via the Internet. This finally raised his graduating GPA over the required minimum.


title: Michael Oher

text: Though he received scholarship offers from Tennessee, LSU, Alabama, Auburn, and South Carolina, Oher ultimately decided to play for Ed Orgeron at the University of Mississippi, the alma mater of his guardians, Leigh Anne and Sean Tuohy. His decision to play for the Ole Miss Rebels football team sparked an investigation by the National Collegiate Athletic Association (NCAA). The first issue was that Oher's grade-point average (GPA) was still too low to meet the requirements for a Division I scholarship at the time of the offer from Ole Miss. That difficulty was corrected by graduation, when Oher completed online classes through Brigham Young University. The second issue was the Tuohys' preexisting relationship with the school and the fact that Ole Miss hired Freeze twenty days after Oher signed his letter of intent. Freeze asserted that his position with Ole Miss was not an example of quid pro quo for encouraging Oher to attend the school, but rather the result of his preexisting relationship with Ole Miss offensive coordinator Noel Mazzone. The NCAA did not close its case on its suspicions of collusion. However, it ruled that Ole Miss had committed no NCAA violations in its recruitment of Oher. Freeze was found guilty of secondary violations for contacting other Memphis-area recruits before joining the Ole Miss staff.


title: Michael Oher

text: Oher started in ten games as a guard during his first season with the Ole Miss Rebels, becoming a first-team freshman All-American. After shifting to the position of left tackle for the 2006 season, he was named to various preseason All-Conference and All-American teams. Oher was named a second-team Southeastern Conference (SEC) offensive lineman after his sophomore season and a first-team SEC offensive lineman after his junior season. Oher was also successful academically at Ole Miss, and his tested IQ score increased 20 to 30 points between when he was measured in the public-school systems growing up and when he was measured in college.


title: Michael Oher

text: On January 14, 2008, Oher declared that he would be entering the 2008 NFL Draft. However, two days later, he announced his withdrawal from the draft to return to Ole Miss for his senior season. After the 2008 season, Oher was recognized as a unanimous first-team All-American, made the honor roll for the second time (the first time being his sophomore year), and graduated with a degree in criminal justice in the spring of 2009.


title: Michael Oher

text: Already in 2008, Oher was projected as one of the top prospects for the 2009 NFL Draft. The Baltimore Ravens drafted Oher with the 23rd pick in the first round of the 2009 NFL Draft. The Ravens had acquired the pick from the New England Patriots in exchange for their first- and fifth-round draft picks. The Tuohy family was there to witness his draft day selection.


title: Michael Oher

text: On July 30, 2009, Oher signed a five-year, $13.8 million contract with the Baltimore Ravens. He started the 2009 season as right tackle, but was moved to left tackle after an injury to lineman Jared Gaither. In week eight, he returned to right tackle.


title: Michael Oher

text: Oher started every game in 2009, eleven at right tackle and five at left tackle. He played right tackle in his first post-season game, January 10, 2010, against the New England Patriots, and did not allow a single sack as the Ravens won 33–14.


title: Michael Oher

text: Oher was second in the voting for Associated Press' NFL Offensive Rookie of the Year Award, with six votes.


title: Michael Oher

text: Prior to the 2010 NFL season, Oher was moved to the left tackle position. During the 2011 pre-season, the Ravens announced that Oher would be moving back to the right side. On February 3, 2013, Oher won his first Super Bowl ring after the Ravens defeated the San Francisco 49ers 34–31 in Super Bowl XLVII.


title: Michael Oher

text: On March 14, 2014, Oher signed a four-year, $20 million contract with the Tennessee Titans. Oher started eleven games for the Titans, but he was placed on injured reserve on December 13 after missing the previous two games due to a toe injury. "Pro Football Focus" graded Oher as the 74th best tackle out of 78 for the 2014 season. The Titans released Oher on February 5, 2015.


title: Michael Oher

text: On March 6, 2015, Oher signed a two-year, $7 million contract with the Carolina Panthers. Dave Gettleman, the Panthers GM, said that Oher would be the Panthers' starting left tackle going into the season despite his struggles in Tennessee, saying "We did our homework on Michael, and we feel very strongly that he can be an answer for us. He'll be inserted at left tackle, and we'll go from there." Oher cited Cam Newton as an influential factor in his decision to sign with Carolina and Oher responded with one of his best seasons as a professional, protecting Newton's blind side. Oher played in 98.4% of the team's snaps, allowed a career-low four sacks—tied for eighth-fewest in the league—and was penalized only three times for 25 yards.


title: Michael Oher

text: On February 7, 2016, Oher was part of the Panthers team that played in Super Bowl 50. In the game, the Panthers fell to the Denver Broncos by a score of 24–10.


title: Michael Oher

text: On June 17, 2016, Oher signed a three-year contract extension with the Panthers worth $21.6 million with $9.5 million guaranteed. Oher was placed on injured reserve on November 25, 2016, with a concussion—having played in only three games during the 2016 season.


title: Michael Oher

text: Oher is one of the subjects of Michael Lewis's 2006 book, "". Before the book was published, excerpts appeared in "The New York Times Magazine" as "The Ballad of Big Mike". His portion of the book was adapted for film and was directed by John Lee Hancock. "The Blind Side" was released in the United States on November 20, 2009. The movie stars Quinton Aaron as Michael Oher, alongside Sandra Bullock and Tim McGraw. The movie was nominated for Academy Awards for both Best Picture and Best Actress for Bullock. Bullock won an Oscar for her portrayal of Leigh Anne Tuohy.


title: Michael Oher

text: Oher wrote his autobiography, "I Beat the Odds: From Homelessness to The Blind Side and Beyond", in 2011.


title: Michael Oher

text: Oher began dating Tiffany Roy after first meeting at the University of Mississippi. They went on to have four children together; two sons and two daughters. The couple got engaged on July 21, 2021, and married on November 5, 2022 in Nashville, Tennessee. At the time of their marriage, the couple had been together for 17 years.


title: Billy Beane

text: William Lamar Beane III (born March 29, 1962) is an American former professional baseball player and current front office executive. He is the executive vice president of baseball operations and minority owner of the Oakland Athletics of Major League Baseball (MLB); he is also minority owner of Barnsley FC of the EFL League One in England and AZ Alkmaar of the Eredivisie in the Netherlands. From 1984 to 1989 he played in MLB as an outfielder for the New York Mets, Minnesota Twins, Detroit Tigers, and Oakland Athletics. He joined the Athletics' front office as a scout in 1990, was named general manager after the 1997 season, and was promoted to executive vice president after the 2015 season.


title: Billy Beane

text: A first-round pick in the MLB draft by the Mets, Beane failed to meet the expectations of scouts, who projected him as a star. In his front-office career, Beane has applied statistical analysis (known as sabermetrics) to baseball, which has led teams to reconsider how they evaluate players. He is the subject of Michael Lewis's 2003 book on baseball economics, "Moneyball", which was made into a 2011 film starring Brad Pitt as Beane.


title: Billy Beane

text: Beane grew up in Mayport, Florida, and San Diego, California, the child of a career military family. His father, a naval officer, taught him how to pitch.


title: Billy Beane

text: Beane attended Mt. Carmel High School in San Diego, where he excelled at baseball, football, and basketball. The high school coach added Beane to the varsity baseball team for the last game of his freshman season. Beane batted .501 during his sophomore and junior years of high school. In his senior season, his batting average dropped to .300.


title: Billy Beane

text: Despite the decrease in batting average, scouts were enamored with Beane's talent. Beane gave up football to avoid an injury that could prematurely end his baseball career. Despite this, Stanford University tried to recruit Beane on a joint baseball–football scholarship as the quarterback who would succeed then-sophomore John Elway for the Stanford Cardinal football team.


title: Billy Beane

text: The New York Mets, who had the first overall selection of the 1980 Major League Baseball Draft, liked Beane's talent and considered choosing him with the first pick. Because many teams believed he would attend Stanford and not sign with a professional team, Beane fell to the 23rd pick, where he was taken by the Mets, who had two other first-round picks that year, allowing them to risk Beane not signing. After visiting the Mets clubhouse, Beane decided to sign with the Mets for a signing bonus. Beane called his decision to sign with the Mets instead of going to Stanford as the "only decision he would ever make in his life about money."


title: Billy Beane

text: Believing Beane to be a more refined player than their top first-round pick, Darryl Strawberry, the Mets assigned Strawberry to play rookie ball with other high school draftees while Beane was assigned to the Little Falls Mets of the Class A New York–Penn League, with players drafted out of college. Beane struggled in his first season, batting .210. He was unable to make the adjustments necessary when playing tougher competition. The Mets promoted Beane to the Lynchburg Mets of the Class A-Advanced Carolina League in 1981. After a solid season, he was promoted to the Jackson Mets of the Class AA Texas League in 1982. While Strawberry was the league's most valuable player, Beane batted .220. Beane began questioning himself, while his new roommate, Lenny Dykstra, succeeded with unwavering confidence and superior mental focus.


title: Billy Beane

text: Beane remained in Jackson until 1984, when he received his first promotion to MLB, appearing in five games for the 1984 New York Mets. In 1985, Beane spent most of the season with the Tidewater Tides of the Class AAA International League, getting called up to the 1985 Mets for eight games. He batted .284 for the Tides in 1985, leading the team with 19 home runs and 77 runs batted in. Following the season, the Mets traded Beane with Joe Klink and Bill Latham to the Minnesota Twins for Tim Teufel and Pat Crosby, a minor league player.


title: Billy Beane

text: The Twins entered spring training prepared to give Beane the job as their starting left fielder over incumbent Mickey Hatcher, but he dealt with injuries and ineffectiveness. Beane appeared in 80 games for the 1986 Minnesota Twins, batting .216. He also appeared in 32 games for the Toledo Mud Hens of the International League. The Twins sent Beane to their new Class-AAA affiliate, the Portland Beavers of the Pacific Coast League (PCL), after spring training in 1987. After batting .285 for Portland, Beane received a call-up to the Twins after the September 1 roster expansion. He appeared in 12 games for the 1987 Minnesota Twins.


title: Billy Beane

text: The Twins traded Beane to the Detroit Tigers for Balvino Gálvez during spring training in 1988. He made the Tigers' opening-day roster that season as an injury fill-in, and was optioned in late April to Toledo, now serving as Detroit's Class-AAA affiliate, where he spent most of the season. During this time, he played in the same outfield as another player with nearly the same name—Billy Bean—and also had a teammate with the name Rice. Beane appeared in six games for the 1988 Tigers. Granted free agency after the 1988 season, Beane signed with the Oakland Athletics, appearing in 37 games with the 1989 Athletics, batting .241 in 79 at-bats. Beane spent most of the season with the Class-AAA Tacoma Tigers of the PCL. He re-signed with the Athletics for the 1990 season, and was sent down to the minor leagues at the end of spring training.


title: Billy Beane

text: Weary of the lifestyle of a minor-league player, Beane approached Athletics GM Sandy Alderson a day after he was reassigned to minor league camp in April 1990 for a job as an advance scout. Beane held that position through 1993, when he was promoted to assistant GM of the Athletics, tasked with scouting minor-league players.


title: Billy Beane

text: Under the ownership of Walter A. Haas Jr., the Athletics appeared in three consecutive World Series from 1988 through 1990, and had the highest payroll in baseball in 1991. Haas died in 1995, and new owners Stephen Schott and Ken Hofmann ordered Alderson to slash payroll. To field a competitive roster on a limited budget, Alderson began focusing on sabermetric principles to obtain undervalued players. He valued on-base percentage among hitters. Alderson taught Beane to find value that other teams did not see using sabermetrics.


title: Billy Beane

text: Beane succeeded Alderson as GM on October 17, 1997. He continued Alderson's crafting of the Athletics into one of the most cost-effective teams in baseball. For example, in the 2006 MLB season, the Athletics ranked 24th of 30 major league teams in player salaries but had the 5th-best regular-season record.


title: Billy Beane

text: The Athletics reached the playoffs in four consecutive years from 2000 through 2003, losing in the American League Division Series each year. In 2002, the Athletics became the first team in the 100+ years of American League baseball to win 20 consecutive games. They won their first playoff series under Beane in 2006 when they swept the Minnesota Twins in the American League Division Series, but were swept by the Detroit Tigers in the American League Championship Series.


title: Billy Beane

text: After the 2002 season, the Boston Red Sox made Beane an offer of $12.5 million to become their GM, but he declined. On April 15, 2005, Beane received a contract extension to remain with the Athletics as its general manager through 2012, and new team owner Lewis Wolff awarded Beane a small portion of the team's ownership. In February 2012, the Athletics extended Beane's contract through 2019.


title: Billy Beane

text: From their 2006 playoff appearance until 2012, the Athletics did not make the playoffs or finish above .500, which triggered criticism of Beane and his approach in some quarters, especially in 2009. Beane largely dismisses criticism of his approach, indicating that his philosophy revolves around research and analysis. Many other general managers have followed Beane's strategy and now use similar approaches.


title: Billy Beane

text: "Moneyball" has changed how players are valued, and Beane had begun concentrating on high school players, a group he once largely ignored, in the MLB draft, considering them to be heavily undervalued. He and other like-minded GMs also changed their draft strategies to focus more on defensive skills, which became undervalued in the years immediately after the "Moneyball" revolution. This new emphasis on defense was displayed in the 2010 season; although the Athletics finished at .500 and again missed the playoffs, they led MLB in defensive efficiency, measured as the percentage of balls put into play by opponents that resulted in outs, and allowed the fewest runs in the AL. In the 2012 season the Athletics again made the playoffs under Beane, winning the American League West title on the last day of the regular season. The Athletics returned to the playoffs in 2013 by winning the American League West division title again, the team's first back-to-back division championships since the 2002 and 2003 seasons.


title: Billy Beane

text: In December 2009, "Sports Illustrated" named Beane #10 on its list of the Top 10 GMs/Executives of the Decade in all sports.


title: Billy Beane

text: On October 5, 2015, the Athletics announced that Beane had been promoted to executive vice president of baseball operations. Assistant GM David Forst assumed the job of general manager.


title: Billy Beane

text: When the Athletics ownership group agreed to purchase the reincarnation of the San Jose Earthquakes of Major League Soccer, Beane, who has expressed a passion for soccer, began developing a system for objectively analyzing soccer players. He has agreed to help the Earthquakes front office develop a method for building a cost-effective team, as the salary cap in MLS is even more restrictive than the Athletics status as a small-market team in Major League Baseball. However, a system has yet to be implemented.


title: Billy Beane

text: Beane has regarded Arsenal's former manager Arsène Wenger as a personal idol. Beane has held discussions with Wenger, former Manchester United F.C. manager Sir Alex Ferguson, and Liverpool F.C. owner John W. Henry. His friendship with ex-Arsenal scout Damien Comolli and Arsenal owner Stan Kroenke allowed him to delve deep into the world of English soccer.


title: Billy Beane

text: In March 2015, the Dutch soccer club AZ Alkmaar, under general director Robert Eenhoorn, a former major leaguer, hired Beane as an advisor. On December 19, 2017, Beane became part of a consortium led by Chien Lee to purchase Barnsley Football Club, which plays in the EFL League One, the third tier of the English football league system.


title: Billy Beane

text: On January 4, 2007, the software company NetSuite named Beane to its board of directors. NetSuite co-founder Evan Goldberg cited Beane's ability to combine facts with instinct as an important factor in the decision to involve him in the company. Beane also served as a consultant for, and also appears in, the video game "MLB Front Office Manager".


title: Billy Beane

text: Author Michael Lewis made Beane the subject of his 2003 best-selling book "Moneyball: The Art of Winning an Unfair Game". The book explores Beane's methods as the GM of the Athletics and how he, along with Paul DePodesta, used sabermetric principles to field a winning team despite an exceptionally low payroll. The book and Beane's methods have influenced the way many teams and players think about the game of baseball.


title: Billy Beane

text: The book was made into the 2011 film "Moneyball", in which Beane was portrayed by Brad Pitt. Pitt's performance in the film earned him an Oscar nomination for Best Actor.


title: Billy Beane

text: Beane attended the University of California, San Diego, during the baseball off-seasons of his playing career.


title: Bosnian War

text: The Bosnian War ( / Рат у Босни и Херцеговини) was an international armed conflict that took place in Bosnia and Herzegovina between 1992 and 1995. The war is commonly seen as having started on 6 April 1992, following a number of earlier violent incidents. The war ended on 14 December 1995 when the Dayton accords were signed. The main belligerents were the forces of the Republic of Bosnia and Herzegovina and those of Herzeg-Bosnia and Republika Srpska, proto-states led and supplied by Croatia and Serbia, respectively.


title: Bosnian War

text: The war was part of the breakup of Yugoslavia. Following the Slovenian and Croatian secessions from the Socialist Federal Republic of Yugoslavia in 1991, the multi-ethnic Socialist Republic of Bosnia and Herzegovina – which was inhabited by mainly Muslim Bosniaks (44%), Orthodox Serbs (32.5%) and Catholic Croats (17%) – passed a referendum for independence on 29 February 1992. Political representatives of the Bosnian Serbs boycotted the referendum, and rejected its outcome. Anticipating the outcome of the referendum boycotted by the majority of Bosnian Serbs, the Assembly of the Serb People in Bosnia and Herzegovina adopted the Constitution of the Serbian Republic of Bosnia and Herzegovina on 28 February 1992. Following Bosnia and Herzegovina's declaration of independence (which gained international recognition) and following the withdrawal of Alija Izetbegović from the previously signed Cutileiro Plan (which proposed a division of Bosnia into ethnic cantons), the Bosnian Serbs, led by Radovan Karadžić and supported by the Serbian government of Slobodan Milošević and the Yugoslav People's Army (JNA), mobilised their forces inside Bosnia and Herzegovina in order to secure ethnic Serb territory. Then war soon spread across the country, accompanied by ethnic cleansing.


title: Bosnian War

text: The conflict was initially between Yugoslav Army units in Bosnia which later transformed into the Army of Republika Srpska (VRS) on the one side, and the Army of the Republic of Bosnia and Herzegovina (ARBiH), largely composed of Bosniaks, and the Croat forces in the Croatian Defence Council (HVO) on the other side. Tensions between Croats and Bosniaks increased throughout late 1992, resulting in the escalation of the Croat–Bosniak War in early 1993. The Bosnian War was characterised by bitter fighting, indiscriminate shelling of cities and towns, ethnic cleansing, and systematic mass rape, mainly perpetrated by Serb, and to a lesser extent, Croat and Bosniak forces. Events such as the siege of Sarajevo and the Srebrenica massacre later became iconic of the conflict.


title: Bosnian War

text: The Serbs, although initially militarily superior due to the weapons and resources provided by the JNA, eventually lost momentum as the Bosniaks and Croats allied against the Republika Srpska in 1994 with the creation of the Federation of Bosnia and Herzegovina following the Washington agreement. Pakistan ignored the UN's ban on supply of arms, and airlifted anti tank missiles to the Bosnian Muslims, while after the Srebrenica and Markale massacres, NATO intervened in 1995 with Operation Deliberate Force targeting the positions of the Army of the Republika Srpska, which proved key in ending the war. The war ended after the signing of the General Framework Agreement for Peace in Bosnia and Herzegovina in Paris on 14 December 1995. Peace negotiations were held in Dayton, Ohio, and were finalised on 21 November 1995.


title: Bosnian War

text: By early 2008, the International Criminal Tribunal for the former Yugoslavia convicted forty-five Serbs, twelve Croats, and four Bosniaks of war crimes in connection with the war in Bosnia. Estimates suggest around 100,000 people were killed during the war. Over 2.2 million people were displaced, making it, at the time, the most devastating conflict in Europe since the end of World War II. In addition, an estimated 12,000–50,000 women were raped, mainly carried out by Serb forces, with most of the victims being Bosniak women.


title: Bosnian War

text: Clashes between Muslims, Croats, and Serbs in Bosnia started in late February 1992, and "full-scale hostilities had broken out by 6 April", the same day the United States and European Economic Community (EEC) recognised Bosnia and Herzegovina. Misha Glenny gives a date of 22 March, Tom Gallagher gives 2 April, while Mary Kaldor and Laura Silber and Allan Little give 6 April. Philip Hammond claimed the most common view is that the war started on April 6, 1992.


title: Bosnian War

text: Serbs consider the Sarajevo wedding shooting, when a groom's father was killed on the second day of the Bosnian independence referendum, 1 March 1992, as the first death of the war. The Sijekovac killings of Serbs took place on 26 March and the Bijeljina massacre (of mostly Bosniaks) on 1–2 April. On 5 April, after protesters approached a barricade, a demonstrator was killed by Serb forces.


title: Bosnian War

text: The war was brought to an end by the General Framework Agreement for Peace in Bosnia and Herzegovina, negotiated at Wright-Patterson Air Force Base in Dayton, Ohio between 1 and 21 November 1995 and signed in Paris on 14 December 1995.


title: Bosnian War

text: The war in Bosnia and Herzegovina came about as a result of the breakup of the Socialist Federal Republic of Yugoslavia. A crisis emerged in Yugoslavia as a result of the weakening of the confederational system at the end of the Cold War. In Yugoslavia, the national communist party, the League of Communists of Yugoslavia, lost ideological potency. Meanwhile, ethnic nationalism experienced a renaissance in the 1980s after violence in Kosovo. While the goal of Serbian nationalists was the centralisation of Yugoslavia, other nationalities in Yugoslavia aspired to the federalisation and the decentralisation of the state.


title: Bosnian War

text: Bosnia and Herzegovina, a former Ottoman province, has historically been a multi-ethnic state. According to the 1991 census, 44% of the population considered themselves Muslim (Bosniak), 32.5% Serb and 17% Croat, with 6% describing themselves as Yugoslav.


title: Bosnian War

text: March 1989, the crisis in Yugoslavia deepened after the adoption of amendments to the Serbian Constitution allowing the government of Serbia to dominate the provinces of Kosovo and Vojvodina. Until then, Kosovo and Vojvodina's decision-making was independent, and each autonomous province also had a vote at the Yugoslav federal level. Serbia, under newly elected President Slobodan Milošević, gained control over three out of eight votes in the Yugoslav presidency. With additional votes from Montenegro, Serbia was thus able to heavily influence the decisions of the federal government. This situation led to objections from the other republics and calls for the reform of the Yugoslav Federation.


title: Bosnian War

text: At the 14th Extraordinary Congress of the League of Communists of Yugoslavia, on 20 January 1990, the delegations of the republics could not agree on the main issues facing the Yugoslav federation. As a result, the Slovene and Croatian delegates left the Congress. The Slovene delegation, headed by Milan Kučan, demanded democratic changes and a looser federation, while the Serbian delegation, headed by Milošević, opposed it.


title: Bosnian War

text: In the first multi-party election in Bosnia and Herzegovina, in November 1990, votes were cast largely according to ethnicity, leading to the success of the Bosniak Party of Democratic Action (SDA), the Serb Democratic Party (SDS), and the Croatian Democratic Union (HDZ BiH).


title: Bosnian War

text: Parties divided power along ethnic lines so the President of the Presidency of the Socialist Republic of Bosnia and Herzegovina was a Bosniak, the president of the Parliament was a Serb, and the prime minister a Croat. Separatist nationalist parties attained power in other republics, including Croatia and Slovenia.


title: Bosnian War

text: Meetings were held in early 1991 between the leaders of the six Yugoslav republics and the two autonomous regions to discuss the ongoing crisis in Yugoslavia. The Serbian leadership favoured a federal solution, whereas the Croatian and Slovenian leadership favoured an alliance of sovereign states. Bosnian leader Alija Izetbegović proposed an asymmetrical federation in February, where Slovenia and Croatia would maintain loose ties with the four remaining republics. Shortly after, he changed his position and opted for a sovereign Bosnia as a prerequisite for such a federation.


title: Bosnian War

text: On 25 March, Franjo Tuđman and Serbian President Slobodan Milošević held a meeting in Karađorđevo. The meeting was controversial due to claims by some Yugoslav politicians the two presidents agreed to the partition of Bosnia and Herzegovina.


title: Bosnian War

text: On 6 June, Izetbegović and Macedonian president Kiro Gligorov proposed a weak confederation between Croatia, Slovenia, and a federation of the other four republics. That was rejected by the Milošević administration.


title: Bosnian War

text: On 25 June 1991, Slovenia and Croatia declared independence, leading to an armed conflict in Slovenia called the Ten-Day War, and the escalation of the Croatian War of Independence in areas with a substantial ethnic Serb population. In the second half of 1991, the war intensified in Croatia. The Yugoslav People's Army (JNA) also attacked Croatia from Bosnia and Herzegovina.


title: Bosnian War

text: In July 1991, representatives of the Serb Democratic Party (SDS), including SDS president Radovan Karadžić, Muhamed Filipović, and Adil Zulfikarpašić from the Muslim Bosniak Organisation (MBO), drafted an agreement known as the Zulfikarpašić–Karadžić agreement. This would leave SR Bosnia and Herzegovina in a state union with SR Serbia and SR Montenegro. The agreement was denounced by Croat political parties. Although initially welcoming the initiative, the Izetbegović administration later dismissed the agreement.


title: Bosnian War

text: Between September and November 1991, the SDS organised the creation of six "Serb Autonomous Regions" (SAOs). This was in response to the Bosniaks' steps toward seceding from Yugoslavia. Similar steps were taken by the Bosnian Croats.


title: Bosnian War

text: In August 1991, the European Economic Community hosted a conference in an attempt to prevent Bosnia and Herzegovina from sliding into war.


title: Bosnian War

text: On 25 September 1991, the United Nations Security Council passed Resolution 713, imposing an arms embargo on all former Yugoslav territories. The embargo had little effect on the JNA and Serb forces. By that time, the Croatian forces seized large amounts of weaponry from the JNA during the Battle of the Barracks. The embargo had a significant impact in Bosnia and Herzegovina at the start of the Bosnian War. The Serb forces inherited the armaments and the equipment of the JNA, while the Croat and Bosniak forces obtained arms through Croatia in violation of the embargo.


title: Bosnian War

text: 19 September 1991, the JNA moved extra troops to the area around the city of Mostar. This was protested by the local government. On 20 September 1991, the JNA transferred troops to the front at Vukovar via the Višegrad region of northeastern Bosnia. In response, local Croats and Bosniaks set up barricades and machine-gun posts. They halted a column of 60 JNA tanks, but were dispersed by force the following day. More than 1,000 people had to flee the area. This action, nearly seven months before the start of the Bosnian War, caused the first casualties of the Yugoslav Wars in Bosnia. In the first days of October, the JNA attacked and leveled the Croat village of Ravno in eastern Herzegovina, on their way to attack Dubrovnik in southern Croatia.


title: Bosnian War

text: On 6 October 1991, Bosnian president Alija Izetbegović gave a televised proclamation of neutrality, it included the statement "it is not our war". In the meantime, Izetbegović made the following statement before the Bosnian parliament on 14 October with regard to the JNA: "Do not do anything against the Army. (...) the presence of the Army is a stabilizing factor to us, and we need that Army (...). Until now, we did not have problems with the Army, and we will not have problems later."


title: Bosnian War

text: Throughout 1990, the RAM Plan was developed by SDB and a group of selected Serb officers of the Yugoslav People's Army (JNA) with the purpose of organizing Serbs outside Serbia, consolidating control of the fledgling SDS parties and the positioning of arms and ammunition.


title: Bosnian War

text: The plan was meant to prepare the framework for a third Yugoslavia in which all Serbs with their territories would live together in the same state.


title: Bosnian War

text: Journalist Giuseppe Zaccaria summarised a meeting of Serb army officers in Belgrade in 1992, reporting they had adopted an explicit policy to target women and children as the vulnerable portion of the Muslim religious and social structure. According to some sources, the RAM plan was crafted in the 1980s. Its existence was leaked by Ante Marković, the Prime Minister of Yugoslavia, an ethnic Croat from Bosnia and Herzegovina. The existence and possible implementation of it alarmed the Bosnian government.


title: Bosnian War

text: On 15 October 1991, the parliament of the Socialist Republic of Bosnia and Herzegovina in Sarajevo passed a "Memorandum on the Sovereignty of Bosnia-Herzegovina" by a simple majority. The Memorandum was hotly contested by the Bosnian Serb members of parliament, arguing that Amendment LXX of the Constitution required procedural safeguards and a two-thirds majority for such issues. The Memorandum was debated anyway, leading to a boycott of the parliament by the Bosnian Serbs, and during the boycott the legislation was passed. The Serb political representatives proclaimed the Assembly of the Serb People of Bosnia and Herzegovina on 24 October 1991, declaring that the Serb people wished to remain in Yugoslavia. The Party of Democratic Action (SDA), led by Alija Izetbegović, was determined to pursue independence and was supported by Europe and the U.S. The SDS made it clear that if independence was declared, Serbs would secede as it was their right to exercise self-determination.


title: Bosnian War

text: The HDZ BiH was established as a branch of the ruling party in Croatia, the Croatian Democratic Union (HDZ). While it called for the independence of the country, there was a split in the party with some members advocating secession of Croat-majority areas. In November 1991, the Croat leadership organised autonomous communities in areas with a Croat majority. On 12 November 1991, the Croatian Community of Bosnian Posavina was established in Bosanski Brod. It covered eight municipalities in northern Bosnia. On 18 November 1991, the Croatian Community of Herzeg-Bosnia was established in Mostar. Mate Boban was chosen as its president. Its founding document said: "The Community will respect the democratically elected government of the Republic of Bosnia and Herzegovina for as long as exists the state independence of Bosnia and Herzegovina in relation to the former, or any other, Yugoslavia".


title: Bosnian War

text: Borisav Jović's memoirs show that on 5 December 1991 Milošević ordered the JNA troops in BiH to be reorganised and its non-Bosnian personnel to be withdrawn, in case recognition would result in the perception of the JNA as a foreign force; Bosnian Serbs would remain to form the nucleus of a Bosnian Serb army. Accordingly, by the end of the month only 10–15% of the personnel in the JNA in BiH was from outside the republic. Silber and Little note that Milošević secretly ordered all Bosnian-born JNA soldiers to be transferred to BiH. Jović's memoirs suggest that Milošević planned for an attack on Bosnia well in advance.


title: Bosnian War

text: On 9 January 1992, the Bosnian Serbs proclaimed the "Republic of the Serbian People in Bosnia-Herzegovina" (SR BiH, later Republika Srpska), but did not officially declare independence. The Arbitration Commission of the Peace Conference on Yugoslavia in its 11 January 1992 Opinion No. 4 on Bosnia and Herzegovina stated that the independence of Bosnia and Herzegovina should not be recognised because the country had not yet held a referendum on independence.


title: Bosnian War

text: On 25 January 1992, an hour after the session of parliament was adjourned, the parliament called for a referendum on independence on 29 February and 1 March. The debate had ended after Serb deputies withdrew after the majority Bosniak–Croat delegates turned down a motion that the referendum question be placed before the not yet established Council of National Equality. The referendum proposal was adopted in the form as proposed by Muslim deputies, in the absence of SDS members. As Burg and Shoup note, "the decision placed the Bosnian government and the Serbs on a collision course". The upcoming referendum caused international concern in February.


title: Bosnian War

text: The Croatian War would result in United Nations Security Council Resolution 743 on 21 February 1992, which created the United Nations Protection Force (UNPROFOR).


title: Bosnian War

text: During the talks in Lisbon on 21–22 February a peace plan was presented by EC mediator José Cutileiro, which proposed the independent state of Bosnia to be divided into three constituent units. Agreement was denounced by the Bosniak leadership on 25 February. On 28 February 1992, the Constitution of the SR BiH declared that the territory of that Republic included "the territories of the Serbian Autonomous Regions and Districts and of other Serbian ethnic entities in Bosnia and Herzegovina, including the regions in which the Serbian people remained in the minority due to the genocide conducted against it in World War II", and it was declared to be a part of Yugoslavia.


title: Bosnian War

text: The Bosnian Serb assembly members advised Serbs to boycott the referendums held on 29 February and 1 March 1992. The turnout to the referendums was reported as 63.7%, with 92.7% of voters voting in favour of independence (implying that Bosnian Serbs, which made up approximately 34% of the population, largely boycotted the referendum). The Serb political leadership used the referendums as a pretext to set up roadblocks in protest. Independence was formally declared by the Bosnian parliament on 3 March 1992.


title: Bosnian War

text: During the referendum on 1 March, Sarajevo was quiet except for a shooting on a Serbian wedding. The brandishing of Serbian flags in the Baščaršija was seen by Muslims as a deliberate provocation on the day of the referendum, which was supported by most Bosnian Croats and Muslims but boycotted by most of the Bosnian Serbs. Nikola Gardović, the bridegroom's father, was killed, and a Serbian Orthodox priest was wounded. Witnesses identified the killer as Ramiz Delalić, also known as "Ćelo", a minor gangster who had become an increasingly brazen criminal since the fall of communism and was also stated to have been a member of the Bosniak paramilitary group "Green Berets". Arrest warrants were issued against him and another suspected assailant. SDS denounced the killing and claimed that the failure to arrest him was due to SDA or Bosnian government complicity. A SDS spokesman stated it was evidence that Serbs were in mortal danger and would be further so in an independent Bosnia, which was rejected by Sefer Halilović, founder of the Patriotic League, who stated that it was not a wedding but a provocation and accused the wedding guests of being SDS activists. Barricades appeared in the following early morning at key transit points across the city and were manned by armed and masked SDS supporters.


title: Bosnian War

text: Following Bosnia and Herzegovina's declaration of independence from Yugoslavia on 3 March 1992, sporadic fighting broke out between Serbs and government forces all across the territory.


title: Bosnian War

text: On 18 March 1992, all three sides signed the Lisbon Agreement: Alija Izetbegović for the Bosniaks, Radovan Karadžić for the Serbs and Mate Boban for the Croats. However, on 28 March 1992, Izetbegović, after meeting with the then-US ambassador to Yugoslavia Warren Zimmermann in Sarajevo, withdrew his signature and declared his opposition to any type of ethnic division of Bosnia.


title: Bosnian War

text: In late March 1992, there was fighting between Serbs and combined Croat and Bosniak forces in and near Bosanski Brod, resulting in the killing of Serb villagers in Sijekovac. Serb paramilitaries committed the Bijeljina massacre, most of the victims of which were Bosniaks, on 1–2 April 1992.


title: Bosnian War

text: The three ethnic groups predominantly supported their respective ethnic or national faction: Bosniaks mainly the ARBiH, Croats the HVO, Serbs the VRS. There were foreign volunteers in each faction.


title: Bosnian War

text: The Bosnians mainly organised into the Army of the Republic of Bosnia and Herzegovina ("", ARBiH) as the armed forces of the Republic of Bosnia and Herzegovina. Forces of the Republic of Bosnia and Herzegovina were divided into five Corps. 1st Corps operated in the region of Sarajevo and Goražde, while the stronger 5th Corps was positioned in the western Bosanska Krajina pocket, which cooperated with HVO units in and around Bihać. The Bosnian government forces were poorly equipped and unprepared for war.


title: Bosnian War

text: Sefer Halilović, Chief of Staff of the Bosnian Territorial Defense, claimed in June 1992 that his forces were 70% Muslim, 18% Croat and 12% Serb. The percentage of Serb and Croat soldiers in the Bosnian Army was particularly high in Sarajevo, Mostar and Tuzla. The deputy commander of the Bosnian Army's Headquarters, was general Jovan Divjak, the highest-ranking ethnic Serb in the Bosnian Army. General Stjepan Šiber, an ethnic Croat was the second deputy commander. Izetbegović also appointed colonel Blaž Kraljević, commander of the Croatian Defence Forces in Herzegovina, to be a member of Bosnian Army's Headquarters, seven days before Kraljević's assassination, in order to assemble a multi-ethnic pro-Bosnian defense front. This diversity was to reduce over the course of the war.


title: Bosnian War

text: The Bosnian government lobbied to have the arms embargo lifted, but that was opposed by the United Kingdom, France and Russia. U.S. proposals to pursue this policy were known as lift and strike. The US congress passed two resolutions calling for the embargo to be lifted, but both were vetoed by President Bill Clinton for fear of creating a rift between the US and the aforementioned countries. Nonetheless, the United States used both "black" C-130 transports and back channels, including Islamist groups, to smuggle weapons to Bosnian-Muslim forces, as well as allowed Iranian-supplied arms to transit through Croatia to Bosnia. However, in light of widespread NATO opposition to American (and possibly Turkish) endeavors in coordinating the "black flights of Tuzla", the United Kingdom and Norway expressed disapproval of these measures and their counterproductive effects on NATO enforcement of the arms embargo.


title: Bosnian War

text: Pakistan's Inter-Services Intelligence also played an active role during 1992–1995 and secretly supplied the Muslim fighters with arms, ammunition and guided anti tank missiles to give them a fighting chance against the Serbs. Pakistan was thus defying the UN ban on supplying arms to Bosnian Muslims, and General Javed Nasir later claimed that the ISI had airlifted anti-tank guided missiles to Bosnia, which ultimately turned the tide in favour of Bosnian Muslims and forced the Serbs to lift the siege.


title: Bosnian War

text: In his book "The Clinton Tapes: Wrestling History with the President" from 2009, historian and author Taylor Branch, a friend of U.S. President Bill Clinton, made public more than 70 recorded sessions with the president during his presidency from 1993 through 2001. According to a session taped on 14 October 1993, it is stated that:


title: Bosnian War

text: The Croats started organizing their military forces in late 1991. On 8 April 1992, the Croatian Defence Council (, HVO) was founded as the "supreme body of Croatian defence in Herzeg-Bosnia". The HVO was organised in four Operative Zones with headquarters in Mostar, Tomislavgrad, Vitez and Orašje. In February 1993, the HVO Main Staff estimated the strength of the HVO at 34,080 officers and men. Its armaments included around 50 main battle tanks, mainly T-34 and T-55, and 500 various artillery weapons.


title: Bosnian War

text: At the beginning of the war, the Croatian government helped arm both the Croat and Bosniak forces. Logistics centres were established in Zagreb and Rijeka for the recruitment of soldiers for the ARBiH. The Croatian National Guard (Zbor Narodne Garde, ZNG), later renamed officially to Croatian Army (, HV) was engaged in Bosnian Posavina, Herzegovina and Western Bosnia against the Serb forces. During the Croat-Bosniak conflict, the Croatian government provided arms for the HVO and organised the sending of units of volunteers, with origins from Bosnia and Herzegovina, to the HVO.


title: Bosnian War

text: The Croatian Defence Forces (HOS), the paramilitary wing of the Croatian Party of Rights, fought against the Serb forces together with the HVO and ARBiH. The HOS was disbanded shortly after the death of their commander Blaž Kraljević and incorporated into the HVO and ARBiH.


title: Bosnian War

text: The Army of Republika Srpska ("", VRS) was established on 12 May 1992. It was loyal to Republika Srpska, the Serbian portion of Bosnia which did not wish to break away from FR Yugoslavia. Bosnian Serb political leader Radovan Karadžić stated "Our optimum is a Greater Serbia, and if not that, then a Federal Yugoslavia".


title: Bosnian War

text: Serbia provided logistical support, money and supplies to the VRS. Bosnian Serbs had made up a substantial part of the JNA officer corps. Milošević relied on the Bosnian Serbs to win the war themselves. Most of the command chain, weaponry, and higher-ranked military personnel, including General Ratko Mladić, were from the JNA.


title: Bosnian War

text: Various paramilitary units operated during the Bosnian War: the Serb "White Eagles" ("Beli Orlovi") and "Serbian Volunteer Guard" ("Srpska Dobrovoljačka Garda"), also known as "Arkan's Tigers"; the Bosnian "Patriotic League" ("Patriotska Liga") and "Green Berets" ("Zelene Beretke"); and Croat "Croatian Defence Forces" ("Hrvatske Obrambene Snage"), etc. The Serb and Croat paramilitaries involved volunteers from Serbia and Croatia, and were supported by nationalist political parties in those countries.


title: Bosnian War

text: The war attracted foreign fighters and mercenaries from various countries. Volunteers came to fight for a variety of reasons, including religious or ethnic loyalties and in some cases for money. As a general rule, Bosniaks received support from Islamic countries, Serbs from Eastern Orthodox countries, and Croats from Catholic countries. The presence of foreign fighters is well documented, however none of these groups comprised more than 5 percent of any of the respective armies' total manpower strength.


title: Bosnian War

text: The Bosnian Serbs received support from Christian Slavic fighters from various countries in Eastern Europe, including volunteers from other Orthodox Christian countries. These included hundreds of Russians, around 100 Greeks, and some Ukrainians and Romanians. Some estimate as many as 1,000 such volunteers. Greek volunteers of the Greek Volunteer Guard were reported to have taken part in the Srebrenica Massacre, with the Greek flag being hoisted in Srebrenica when the town fell to the Serbs.


title: Bosnian War

text: Some individuals from other European countries volunteered to fight for the Croat side, including Neo-Nazis such as Jackie Arklöv, who was charged with war crimes upon his return to Sweden. Later he confessed he committed war crimes on Bosnian Muslim civilians in the Heliodrom and Dretelj camps as a member of Croatian forces.


title: Bosnian War

text: The Bosnians received support from Muslim groups. Pakistan supported Bosnia while providing technical and military support. Pakistan's Inter-Services Intelligence (ISI) allegedly ran an active military intelligence program during the Bosnian War which started in 1992 lasting until 1995. Executed and supervised by Pakistani General Javed Nasir, the program provided logistics and ammunition supplies to various groups of Bosnian mujahideen during the war. The ISI Bosnian contingent was organised with financial assistance provided by Saudi Arabia, according to the British historian Mark Curtis.


title: Bosnian War

text: According to The Washington Post, Saudi Arabia provided $300 million in weapons to government forces in Bosnia with the knowledge and tacit cooperation of the United States, a claim denied by US officials. Foreign Muslim fighters also joined the ranks of the Bosnian Muslims, including from the Lebanese guerrilla organisation Hezbollah, and the global organization al-Qaeda.


title: Bosnian War

text: During the war in Croatia, arms had been pouring into Bosnia. The JNA armed Bosnian Serbs, and the Croatian Defence Force armed Herzegovinian Croats. The Bosnian Muslim Green Berets and Patriotic League were already established in the autumn of 1991, and drew up a defense plan in February 1992. It was estimated that 250–300,000 Bosnians were armed, and that some 10,000 were fighting in Croatia. By March 1992, perhaps three-quarters of the country were claimed by Serb and Croat nationalists. On 4 April 1992, Izetbegović ordered all reservists and police in Sarajevo to mobilise, and SDS called for evacuation of the city's Serbs, marking the "definite rupture between the Bosnian government and Serbs". Bosnia and Herzegovina received international recognition on 6 April 1992. The most common view is that the war started that day.


title: Bosnian War

text: The war in Bosnia escalated in April. On 3 April, the Battle of Kupres began between the JNA and a combined HV-HVO force that ended in a JNA victory. On 6 April Serb forces began shelling Sarajevo, and in the next two days crossed the Drina from Serbia proper and besieged Muslim-majority Zvornik, Višegrad and Foča. According to the International Criminal Tribunal for the former Yugoslavia, in 1992, after the capture of Zvornik, Bosnian Serb troops killed several hundred Muslims and forced tens of thousands to flee the area. All of Bosnia was engulfed in war by mid-April. On 23 April, the JNA evacuated its personnel by helicopter from the barracks in Čapljina, which had been blockaded since 4 March. There were some efforts to halt violence. On 27 April, the Bosnian government ordered the JNA to be put under civilian control or expelled, which was followed by a series of conflicts in early May between the two. Prijedor was taken over by Serbs on 30 April. On 2 May, the Green Berets and local gang members fought back a disorganised Serb attack aimed at cutting Sarajevo in two. On 3 May, Izetbegović was kidnapped at the Sarajevo airport by JNA officers, and used to gain safe passage of JNA troops from downtown Sarajevo. However, Bosnian forces attacked the departing JNA convoy, which embittered all sides. A cease-fire and agreement on evacuation of the JNA was signed on 18 May, and on 20 May the Bosnian presidency declared the JNA an occupation force.


title: Bosnian War

text: The Army of Republika Srpska was newly established and put under the command of General Ratko Mladić, in a new phase of the war. Shellings on Sarajevo on 24, 26, 28 and 29 May were attributed to Mladić by UN Secretary-General Boutros Boutros-Ghali. Civilian casualties of a 27 May shelling of the city led to Western intervention, in the form of sanctions imposed on 30 May through United Nations Security Council Resolution 757. That same day Bosnian forces attacked the JNA barracks in the city, which was followed by heavy shelling. On 5 and 6 June the last JNA personnel left the city during heavy street fighting and shelling. The 20 June cease-fire, executed in order for UN takeover of the Sarajevo airport for humanitarian flights, was broken as both sides battled for control of the territory between the city and airport. The airport crisis led to Boutros-Ghali's ultimatum on 26 June, that the Serbs stop attacks on the city, allow the UN to take control of the airport, and place their heavy weapons under UN supervision. Meanwhile, media reported that Bush considered the use of force in Bosnia. World public opinion was "decisively and permanently against the Serbs" following media reports on the sniping and shelling of Sarajevo.


title: Bosnian War

text: Outside of Sarajevo, the combatants' successes varied greatly in 1992. Serbs had seized Muslim-majority cities along the Drina and Sava rivers and expelled their Muslim population within months. A joint Bosnian–HVO offensive in May, having taken advantage of the confusion following JNA withdrawal, reversed Serb advances into Posavina and central Bosnia. The offensive continued southwards, besieging Doboj, thereby cutting off Serb forces in Bosanska Krajina from Semberija and Serbia. In mid-May, Srebrenica was retaken by Bosnian forces under Naser Orić. Serb forces suffered a costly defeat in eastern Bosnia in May, when according to Serbian accounts Avdo Palić's force was ambushed near Srebrenica, killing 400. From May to August, Goražde was besieged by the VRS, until the siege was broken by the ARBiH on 1 September. In April 1992, Croatian Defence Council (HVO) entered the town of Orašje and, according to Croatian sources, began a mass campaign of harassment against local Serb civilians, including torture, rape and murder.


title: Bosnian War

text: On 15 May 1992, a JNA column was ambushed in Tuzla. 92nd Motorised JNA Brigade (stationed in "Husinska buna" barracks in Tuzla) received orders to leave the city of Tuzla and Bosnia-Herzegovina, and to enter Serbia. An agreement was made with the Bosnian government that JNA units would be allowed until 19 May to leave Bosnia peacefully. Despite the agreement, the convoy was attacked in Tuzla's Brčanska Malta district with rifles and rocket launchers; mines were also placed along its route. 52 JNA soldiers were killed and over 40 were wounded, most of them ethnic Serbs.


title: Bosnian War

text: The Republic of Bosnia and Herzegovina was admitted as a member State of the United Nations on 22 May 1992.


title: Bosnian War

text: From May to December 1992, the Bosnian Ministry of the Interior (BiH MUP), Croatian Defence Council (HVO) and later the Bosnian Territorial Defence Forces (TO RBiH) operated the Čelebići prison camp. It was used to detain 700 Bosnian Serb prisoners of war arrested during military operations that were intended to de-block routes to Sarajevo and Mostar in May 1992 which had earlier been blocked by Serb forces. Of these 700 prisoners, 13 died while in captivity. Detainees at the camp were subjected to torture, sexual assaults, beatings and otherwise cruel and inhuman treatment. Certain prisoners were shot and killed or beaten to death.


title: Bosnian War

text: On 6 May 1992, Mate Boban met with Radovan Karadžić in Graz, Austria, where they reached an agreement for a ceasefire and discussed the details of the demarcation between a Croat and Serb territorial unit in Bosnia and Herzegovina. However, the ceasefire was broken on the following day when the JNA and Bosnian Serb forces mounted an attack on Croat-held positions in Mostar. In June 1992, Bosnian Serb forces attacked and pounded the small Bosnian village of Žepa, and would lead to the three-year long siege of Žepa.


title: Bosnian War

text: By June 1992, the number of refugees and internally displaced persons had reached 2.6 million. By September 1992, Croatia had accepted 335,985 refugees from Bosnia and Herzegovina, mostly Bosniak civilians (excluding men of drafting age). The large number of refugees significantly strained the Croatian economy and infrastructure. Then-U.S. Ambassador to Croatia, Peter Galbraith, tried to put the number of Muslim refugees in Croatia into a proper perspective in an interview on 8 November 1993. He said the situation would be the equivalent of the United States taking in 30,000,000 refugees. The number of Bosnian refugees in Croatia was at the time surpassed only by the number of the internally displaced persons within Bosnia and Herzegovina itself, at 588,000. Serbia took in 252,130 refugees from Bosnia, while other former Yugoslav republics received a total of 148,657 people.


title: Bosnian War

text: In June 1992, the Bosnian Serbs started Operation Corridor in northern Bosnia against HV–HVO forces, to secure an open road between Belgrade, Banja Luka, and Knin. The reported deaths of twelve newborn babies in Banja Luka hospital due to a shortage of bottled oxygen for incubators was cited as an immediate cause for the action, but the veracity of these deaths has since been questioned. Borisav Jović, a contemporary high-ranking Serbian official and member of the Yugoslav Presidency, has claimed that the report was just wartime propaganda, stating that Banja Luka had two bottled oxygen production plants in its immediate vicinity and was virtually self-reliant in that respect. Operation Corridor began on 14 June 1992, when the 16th Krajina Motorized Brigade of the VRS, aided by a VRS tank company from Doboj, began the offensive near Derventa. The VRS captured Modriča on 28 June, Derventa on 4–5 July, and Odžak on 12 July. The HV–HVO forces were reduced to isolated positions around Bosanski Brod and Orašje, which held out during August and September. The VRS managed to break through their lines in early October and capture Bosanski Brod. Most of the remaining Croat forces withdrew north to Croatia. The HV–HVO continued to hold the Orašje enclave and were able to repel an VRS attack in November.


title: Bosnian War

text: On 21 June 1992, Bosniak forces entered the Bosnian Serb village of Ratkovići near Srebrenica and murdered 24 Serb civilians.


title: Bosnian War

text: In June 1992, the UNPROFOR, originally deployed in Croatia, had its mandate extended into Bosnia and Herzegovina, initially to protect the Sarajevo International Airport. In September, the role of UNPROFOR was expanded to protect humanitarian aid and assist relief delivery in the whole Bosnia and Herzegovina, as well as to help protect civilian refugees when required by the Red Cross.


title: Bosnian War

text: On 4 August 1992, the IV Knight Motorised Brigade of the ARBiH attempted to break through the circle surrounding Sarajevo, and a fierce battle ensued between the ARBiH and the VRS in and around the damaged "FAMOS" factory in the suburb of Hrasnica. The VRS repelled the attack, but failed to take Hrasnica in a decisive counterattack.


title: Bosnian War

text: On 12 August 1992, the name of the Serbian Republic of Bosnia and Herzegovina was changed to Republika Srpska (RS). By November 1992, of eastern Bosnia was under Muslim control.


title: Bosnian War

text: The Croat–Bosniak alliance, formed at the beginning of the war, was often not harmonious. The existence of two parallel commands caused problems in coordinating the two armies against the VRS. An attempt to create a joint HVO and TO military headquarters in mid-April failed. On 21 July 1992, the Agreement on Friendship and Cooperation was signed by Tuđman and Izetbegović, establishing a military cooperation between the two armies. At a session held on 6 August, the Bosnian Presidency accepted HVO as an integral part of the Bosnian armed forces.