A Lie group formulation of Kane’s equations for multibody systems

Abstract

We propose a Lie group approach to formulate the Kane’s equations of motion for multibody systems. This approach regards the set of rigid body transformations as the special Euclidean group SE(3). By expressing rigid body displacements as exponential maps generated from the Lie algebra se(3), it subsequently manipulates rigid body kinematics as convenient matrix operations. With this approach, all the individual quantities involved in Kane’s equations can be computed explicitly in an intrinsic manner, and the motion equations can be obtained systematically and efficiently. An example is presented to illustrate its use and effectiveness.