Geometric aspects of the co-rotational derivative of a continuous motion
(EN)
Kadianakis, N
(EN)
In this work we use a frame-independent version of the co-rotational derivative of a motion, and study the geometry defined by this derivative on classical space-time. This is done in the general framework of derivatives, called Spins, which define a rigid parallel translation of space-like vectors. We express the Spin itself in terms of this translation, and show that for a non-uniform Spin this translation depends on the path. Since the co-rotational derivative is a Spin, its geometry is studied in this context. After showing that the relative vorticity of two motions is the difference of their co-rotational derivatives, we prove that the translation defined by the co-rotational derivative of a motion is path-independent, if and only if the motion is homogeneous.
(EN)
