A Coordinate Frame Useful for Rigid-Body Displacement Metrics

Abstract

This paper presents the definition of a coordinate frame, entitled the principal frame (PF), that is useful for metric calculations on spatial and planar rigid-body displacements. Given a set of displacements and using a point mass model for the moving rigid-body, the PF is determined from the associated centroid and principal axes. It is shown that the PF is invariant with respect to the choice of fixed coordinate frame as well as the system of units used. Hence, the PF is useful for left invariant metric computations. Three examples are presented to demonstrate the utility of the PF.