One theorem about these things states that one form of their motions must be Killing motions; that is a corollary of a theorem that states they only have three degrees of freedom in Minkowski space called the Herglotz-Noether theorem. The most general motion of these objects are called "screw displacements" according to Chasles' theorem, and motions of them are often described using the SE(3) grou
One theorem about these things states that one form of their motions must be Killing motions; that is a corollary of a theorem that states they only have three degrees of freedom in Minkowski space called the Herglotz-Noether theorem. The most general motion of these objects are called "screw displacements" according to Chasles' theorem, and motions of them are often described using the SE(3) group. A generalization of these objects has the condition that they preserve constant distances in the co-moving frame; that generalization is due to (*) Born and extends them to special relativity. A rotating asymmetric one of these has an angular velocity vector that traces out a polhode and a herpolhode, and during torque-free rotation, the kinetic energy of these objects defines a construct that rolls on the invariant plane without slipping; that construct is Poinsot's ellipsoid. Euler angles are used to describe the motion of these objects. For 10 points, give this name for idealized three-dimensional objects that cannot be deformed.
One theorem about these things states that one form of their motions must be Killing motions; that is a corollary of a theorem that states they only have three degrees of freedom in Minkowski space called the Herglotz-Noether theorem.
rigid body [or rigid bodies; anti-prompt on “rigid rotor”]