Noise and dissipation in rigid body motion

TL;DR

This paper explores stochastic geometric mechanics in rigid body motion, focusing on noise structure, dissipation, and statistical properties like attractors and measures, linking mathematical structures to physical phenomena.

Contribution

It introduces a geometric variational approach to noise in rigid bodies, incorporating Lie-Poisson brackets, stochastic coadjoint motion, and dissipation, advancing the understanding of stochastic effects in mechanical systems.

Findings

Characterization of noise via Lie-Poisson brackets

Analysis of stationary solutions of the Fokker-Planck equation

Connection between stochastic dynamics and statistical physics concepts

Abstract

Using the rigid body as an example, we illustrate some features of stochastic geometric mechanics. These features include: i) a geometric variational motivation for the noise structure involving Lie-Poisson brackets and momentum maps, ii) stochastic coadjoint motion with double bracket dissipation, iii) the Lie-Poisson Fokker-Planck description and its stationary solutions, iv) random dynamical systems, random attractors and SRB measures connected to statistical physics.