In two-body systems with this kind of force, the cross product of the position and velocity vectors is constant over time; this is a generalization of the law of areal velocities due to Kepler.
Forces of this type yield solvable trajectories only if they take on one of six general four-term forms, as shown by Broucke; those forms include three monomial forms that have a stability index of plus or minus 2. In systems that experience this type of force, one conserved quantity is the cross product of the binormal vector and angular momentum. The motion of a system with an inverse cubic force of this type is a Cotes spiral, and is one of three cases that is soluble in terms of trigonometric functions rather than (*) elliptic integrals. According to Bertrand's theorem, this type of force can only form closed orbits if it is linear or inverse-square. In two-body systems with this kind of force, the cross product of the position and velocity vectors is constant over time; this is a generalization of the law of areal velocities due to Kepler. For 10 points, name these forces that depend only on the distance between objects and act along the line connecting them.
Forces of this type yield solvable trajectories only if they take on one of six general four-term forms, as shown by Broucke; those forms include three monomial forms that have a stability index of plus or minus 2.
central forces [reverse-prompt on "inverse-square force" until "inverse cubic" is read]