On the Metrics of Rigid Body Displacements for Infinite and Finite Bodies

Abstract

This paper presents a critical analysis of the metric of rigid body displacements obtained from the so-called kinematic mapping. It is shown that this metric is not suitable for finite rigid bodies. The paper also addresses the metrics obtained for the planar group, as it can be regarded as a subgroup of the group of all rigid body displacements, which is denoted here as the Euclidean group. Finally, the paper proposes some metrics for the set of spatial and planar displacements for a finite rigid body, undergoing a finite displacement.