Thomas precession for spin and for a rod

In this paper we obtain the differential equations which describe the rotating rod and precession of the spin of a gyroscope moving along a curved trajectory. Several examples of such motion are considered. The obtained equations differ from the traditional Thomas expression, interpreted as a rotation of the noninertial frame relative to the fixed one. The cause of this disagreement is the fact that, in general, the axes of the moving frame are not orthogonal for the fixed observers. When the velocity changes, the axes’ direction changes, due to both Wigner rotation and Lorentz contraction. In the present paper we take into account both of these factors. It is shown that the vectors representing various physical quantities transform in different ways in the moving reference frame. Thus, the kinematic equations describing the motion of these quantities in a fixed frame are different as well.