Thus, electromagnetic and relativistic effects such as Thomas precession, for instance, can be modeled in the complexified rigid body framework (see ).
Mladenov, "Wigner rotation and Thomas precession: geometric phases and related physical theories," Journal of the Korean Physical Society, vol.
Demonstrating the power and elegance that emerges when Einstein's special theory of relativity is treated integrally with its underlying hyperbolic geometry, he covers Einstein gyrogroups and gyrovector spaces; mathematical tools for hyperbolic geometry; hyperbolic triangles and circles; hyperbolic symplices, hyperplanes, and hyperspheres in n dimensions; hyperbolic ellipses and hyperbolas; and Thomas precession
. He provides chapter-end problems for classroom use or self-evaluation.
Beyond the Einstein addition law and its gyroscopic Thomas precession
: The theory of gyrogroups and gyrovector spaces.
In flat space-time the precession of an accelerated gyroscope is called Thomas Precession
. In a general coordinate system the spin vector in parallel obeys the equation: