Nonlinear effects in Thomas precession due to the interplay of Lorentz contraction and Thomas--Wigner rotation

It is demonstrated that the 3–vector $\text{bs}S$ currently associated to the spin in an inertial frame does not contract, but rather dilates, in the direction of the velocity. The correct vector $\text{bs}T$ is individuated. The equation of motion for the two vectors is shown to contain two terms, a common linear rotation, identified with Thomas precession, and also a nonlinear rotation depending on the direction of the spin itself.