The Two Rigid Body Interaction using Angular Momentum Theory Formulae

TL;DR

This paper introduces a novel formalism for modeling two rigid body interactions using angular momentum theory, employing spherical harmonics and Wigner D-matrices for efficient computation of forces and torques.

Contribution

It presents a new formalism that simplifies and accelerates the simulation of two rigid body dynamics through angular momentum theory and recurrence relations.

Findings

The algorithm is significantly faster than existing methods.

Forces and torques are efficiently computed using ladder operators.

Numerical tests confirm improved computational performance.

Abstract

This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The algorithm benefits from the numerous recurrence relations satisfied by these functions allowing a fast evaluation of the mutual potential. Moreover, forces and torques are straightforwardly obtained by application of ladder operators taken from the angular momentum theory and commonly used in quantum mechanics. A numerical implementation of this algorithm is made. Tests show that the present code is significantly faster than those currently available in literature.