Poisson structures for Mathisson equation

Abstract:
Mathisson equation is a third order ordinary differential equation that govern the motion of a relativistic spherical  top. Alternatively, there exist a fourth order equation of Riewe. Existence of the Lagrange function for these equations was previously investigated by present author. Alternatively, some ad hoc approaches by other authors did start from other Lagrange functions, among them these proposed by Bopp, Honl, Plyushchay and others. We investigate different Poisson structures which follow from different Lagrangians in three- and four-dimensional flat space-time for the third and fourth order equations of the relativistic top.