The Two Rigid Body Interaction using Angular Momentum Theory Formulae

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.

13 pages, 1 figure, submitted to CeMDA on September 28, 2016

References in corpus (2)

• Complete spin and orbital evolution of close-in bodies using a Maxwell viscoelastic rheology
• Figure-Figure Interaction Between Bodies Having Arbitrary Shapes and Mass Distributions: A Power Series Expansion Approach

Cited by in corpus (1)

• Propagation and Estimation of the Dynamical Behaviour of Gravitationally Interacting Rigid Bodies