Motion Variables Leading to Efficient Equations of Motion

Abstract

In order to formulate equations that govern the motion of a mechanical system, the analyst must choose time-dependent variables that characterize the configuration and motion of the system. Generally, the choice of variables made by the analyst has a profound effect on the efficiency of the resulting equations—"efficiency" here referring to relative simplicity, ease of manipulation for purposes of designing automatic con trol systems, and minimal consumption of computer time during numerical solution. In this article, guidelines are set forth for the selection of motion variables that lead to exceptionally effi cient dynamical differential equations for systems belonging to a large class frequently encountered in robotics.