Continuous body dynamics and the Mathisson-Papapetrou-Dixon equations

TL;DR

This paper derives the Mathisson-Papapetrou-Dixon equations from an effective particle Lagrangian, showing how continuous bodies can be modeled as effective particles with spin defined without fixed frames, and explores gauge and center of mass conditions.

Contribution

It introduces a novel derivation of MPD equations from an effective particle perspective and links gauge choices to spin supplementary conditions.

Findings

Effective particle Lagrangian reproduces MPD equations.

Spin can be defined without fixed body frames.

Center of mass condition relates to spin supplementary condition.

Abstract

We show that an effective particle Lagrangian yields the Mathisson-Papapetrou-Dixon (MPD) equations. The spin of the effective particle is defined without any reference to a fixed body frame or angular velocity variable. We then demonstrate that a continuous body, defined by a congruence of world lines and described by a general action, can be rewritten as an effective particle. We analyze the gauge freedom of the body and show that a natural center of mass condition is related to a spin supplementary condition.