This entry is largely based on this paper.
Suppose we have an object going in a circle, such that its orbital angular momentum is . Suppose further that this object is rotating around itself with angular momentum . According to classical mechanics should not change in time, but special relativistic corrections cause to precess around . This is called Thomass precession.
The way to calculate the rate of precession is by considering the action of the centripetal force as a series of infinitesimal boosts in different directions. Classically, if a object was moving at velocity and is then boosted by , its velocity (and hence direction) would be given by . In relativity, however, the application of two Lorentz boosts yields a slightly different velocity
We will be interested in the limit where . The angle between the classical and relativistic directions is given by
By dividing by the time interval in which the boost happens it is possible to get the precession rate, assuming and is the acceleration