A Lie-Group Formulation of Kinematics and Dynamics of Constrained MBS and Its Application to Analytical Mechanics

Abstract

A Lie-group formulation for the kinematics and dynamics ofholonomic constrained mechanical systems (CMS) is presented. The kinematics ofrigid multibody systems (MBS) is described in terms of the screw system of theMBS. Using Lie-algebraic properties of screw algebra, isomorphicto se(3), allows a purely algebraic derivation of the Lagrangian motion equations. As such the Lie-group SE(3) ⊗... ⊗ SE(3) (n copies) is theambient space of a MBS consisting of n rigid bodies. Any parameterizationof the ambient space corresponds to a chart on the MBS configuration space ℝn. The key to combine differential geometric and Lie-algebraic approaches is the existence of kinematic basic functions whichare push forward maps from the tangent bundle Tℝn to the Lie-algebra of the ambient space.