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

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.