Motion of a Rigid Body in Body-Fixed Coordinate System -- for Autoparrallel Trajectories in Spaces with Torsion

TL;DR

This paper derives the equations of motion for a rigid body in a space with curvature and torsion, demonstrating that trajectories follow autoparallels rather than geodesics, challenging common assumptions.

Contribution

It introduces a new action principle for rigid body motion in spaces with torsion, illustrating autoparallel trajectories in such geometries.

Findings

Rigid body trajectories follow autoparallels in torsion spaces

Derived Euler equations using a novel action principle

Challenges the belief that shortest paths are followed in such spaces

Abstract

We use a recently developed action principle in spaces with curvature and torsion to derive the Euler equations of motion for a rigid body within the body-fixed coordinate system. This serves as an example that the particle trajectories in a space with curvature and torsion follow the straightest paths (autoparallels), not the shortest paths (geodesics), as commonly believed.