Numerical implementation of the exact dynamics of free rigid bodies

TL;DR

This paper derives an exact analytical solution for the motion of free rigid bodies with arbitrary mass distribution, providing explicit formulas for orientation and position over time, useful for verification and simulation purposes.

Contribution

It introduces a novel, explicit analytical solution for rigid body dynamics that depends directly on initial conditions and involves only real numbers.

Findings

Provides explicit formulas for rigid body orientation and position over time

Enables efficient calculation of rigid body motion at arbitrary times

Facilitates verification of numerical integrators and development of symplectic methods

Abstract

In this paper the exact analytical solution of the motion of a rigid body with arbitrary mass distribution is derived in the absence of forces or torques. The resulting expressions are cast into a form where the dependence of the motion on initial conditions is explicit and the equations governing the orientation of the body involve only real numbers. Based on these results, an efficient method to calculate the location and orientation of the rigid body at arbitrary times is presented. This implementation can be used to verify the accuracy of numerical integration schemes for rigid bodies, to serve as a building block for event-driven discontinuous molecular dynamics simulations of general rigid bodies, and for constructing symplectic integrators for rigid body dynamics.