Relativistic top in the Ostrohrads'kyj dynamics

TL;DR

This paper develops a fourth-order variational equation for a free relativistic top, derived from Dixon's equations, and reformulates it into a homogeneous space-time Hamiltonian form, advancing the theoretical understanding of relativistic spinning bodies.

Contribution

It introduces a novel fourth-order variational equation for the relativistic top based on Dixon's system and expresses it in Hamiltonian form, providing new theoretical insights.

Findings

Derived a fourth-order variational equation for the relativistic top.

Reformulated the equation into a homogeneous space-time Hamiltonian form.

Enhanced the theoretical framework for relativistic spinning particles.

Abstract

A variational equation of the fourth order for the free relativistic top is developed starting from the Dixon's system of equations for the motion of the relativistic dipole. The obtained equation is then cast into the homogeneous space-time Hamiltonian form.