A covering second-order Lagrangian for the relativistic top without forces

TL;DR

This paper develops a covariant second-order Lagrangian framework for describing the free relativistic top, ensuring parameter invariance and accommodating constant acceleration constraints.

Contribution

It introduces a new covariant second-order variational formulation for the relativistic top without external forces, expanding the theoretical understanding of relativistic spinning bodies.

Findings

Derived a parameter-invariant covariant Lagrangian for the relativistic top

Formulated the problem on a constraint manifold of constant acceleration

Provided a consistent variational approach for free relativistic spinning particles

Abstract

A parameter-invariant variational problem with a manifestly covariant Lagrangian function of second order is considered, which covers the case of the free relativistic top at constraint manifold of constant acceleration