Herglotz–Noether theorem

The Herglotz–Noether theorem in special relativity, named after Gustav Herglotz and Fritz Noether, restricts the possible linear and rotational motions of a Born-rigid object. It was pointed out that the motion of the whole rigid body is in general definitely determined by the arbitrarily defined motion of a single point of it. (According to Herglotz, exceptions only take place when the world-lines have constant curvature.) In consequence, a Born rigid body only has three degrees of freedom.

A more recent expression of the Herglotz–Noether theorem states, that rotational rigid motion in Minkowski space must be a Killing motion.