Quasi-Hamiltonian description of classical spin

TL;DR

This paper introduces a quasi-Hamiltonian framework for classical spinning particles, deriving equations of motion and a generalized Hamiltonian description that satisfy specific physical conditions.

Contribution

It presents a novel quasi-Hamiltonian formulation for classical relativistic spinning particles and extends the Hamilton-Ostrohrads'kyj approach to spherical tops.

Findings

Derived third-order equations of motion for relativistic spinning particles

Proposed a generalized Hamiltonian formalism consistent with Pirani conditions

Established a new Lagrangian family producing these equations

Abstract

A family of Lagrange functions is considered, each producing the classical relativistic free spinning particle equation of motion of the third order. On this grounds a generalized Hamilton-Ostrohrads'kyj description of the free relativistic spherical top is proposed, which comply with the Pirani supplementary conditions.