Max Born

“ There is an instantaneous axis of rotation, i.e. by a suitable Lorentz transformation one can achieve that all points of a straight line are at rest.
6) All points of the body have a constant "rest distance" with respect to a certain point located upon the instantaneous axis, the center of rotation.
Except the identification of these general properties of the definition, I have computed some special motions, among them the case that a point of the body carries out a uniformly-accelerated motion (hyperbolic motion) , and that the body is arbitrarily rotating about the direction of translation. ”

“ However, one has to view as desirable the introduction of a rigidity definition, which represents the completest possible analogy to the rigid body of ordinary kinematics; because on one side the rigid body is necessary for the formation of mechanics, and in addition it seems to me that an electron theory without this concept is an essential step backwards. ”

“ Definition: The motion of a point system is called rigid, when between the location and the velocity of any point the relation persists that the relative velocity towards the center is equal to the rest rotation:
or extensively:
This definition is covariant with respect to Lorentz transformations. Furthermore it is fully sufficient in connection with conditions (17) and (18) , in order to determine the motion as soon as the motion of center and the path of vector are given for all times in agreement with conditions (16) and (19) . ”