Thomas precession by pseudoquaternions
2005jbj | D. E. Burlankov, G. B. Malykin  // Nizhny Novgorod State University; Institute of Applied Physics RAS, Nizhny Novgorod, Russia

When a body moves curvilinearly in a plane with a velocity that is comparable to the velocity of light, only three coordinates of the body undergo Lorentz transformation, and the transformation matrix appears to be three-parametric. This enables description of these transformations by pseudoquaternions, Hamilton quaternions slightly modified for pseudo-Euclidean character of the metrics. Their algebraic properties and relation to the Lorentz transformations in a 2+1-dimensional Minkovsky space were determined. We integrated the pseudoquaternion differential equation of continuous transformations at a body's motion along a circular orbit and, as a result, obtained an expression for the value of the Thomas precession.

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