On the Inertial Rotational Brownian Motion of Arbitrarily Shaped Particles

TL;DR

This paper models the inertial rotational Brownian motion of arbitrarily shaped particles using an Ornstein-Uhlenbeck process on SO(3), enabling analysis without simplifying shape or viscosity assumptions.

Contribution

It introduces a novel modeling approach for rotational Brownian motion of arbitrary particles via an Ornstein-Uhlenbeck process on the cotangent bundle of SO(3).

Findings

The model handles particles with arbitrary shapes.

Approximate solutions to the Fokker-Planck equation are obtained.

The approach avoids simplifying assumptions on particle shape.

Abstract

This article reports the modeling of inertial rotational Brownian motion as an Ornstein-Uhlenbeck process evolving on the cotangent bundle of the rotation group, SO(3). The benefit of this approach and the use of a different parameterization of rotations allows the handling of particles with arbitrary shapes, without requiring any simplifying assumptions on the shape or the structure of the viscosity tensors. The resultant Fokker-Planck equation for the joint orientation and angular momentum probability distribution can be solved approximately using an `ansatz' Gaussian distribution in exponential coordinates.