Investigation of a New Formulation of the Lagrange Method for Constrained Dynamic Systems

Abstract

Lagrange multipliers are often used in order to model constrained dynamic systems. This method results in problems of constraints violations and therefore various methods of constraints stabilization have been presented in the past. The purpose of the present paper is to present a new formulation of the method that stabilizes the constraints, but unlike other stabilization methods it is also consistent within the framework of variational methods. The new formulation can be applied to holonomic or nonholonomic constraints. After the presentation of the new formulation, its application to constrained rigid rod systems is presented. The results of the new method are compared with other stabilization techniques.