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 
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”]