Lagrangian formulation and linearization of multibody system equations

Abstract

Most classical methods of analytical mechanics, when used for setting the equations of multibody systems, lead to heavy and sometimes confused formulations, especially in the case of flexible bodies. Thus the linearization of these equations, to be used for instance in linear control algorithms, may result in a difficult task. The aim of this paper is to show that, through a renewed approach of the body dynamic formulation, the linearization task can be rationally organized. First the single body dynamic equations are established in the context of a Lagrangian formulation, leading to the expressions of the generalized inertial forces and the definition of the constant inertial body characteristics. Then after a careful examination of the mathematical structure of the body equations, a recursive procedure for assembling them and linearizing the global equation is developed. Finally, a practical application of the multibody formulation with linearization is presented, in the framework of a problem of antivibration control.