A Method for Constraints Stabilization on Solving Multibody Dynamics

Abstract

Abstract This paper deals with methods for solving the multibody dynamics with constraints. The problem is considered in the framework of solving the Lagrange multipliers in addition to the system coordinates in the differential and algebraic equation (DAE) governing the dynamics with holonomic or non-holonomic constraints. The proposed methods are originally based on Baumgarte’s work for the holonomic constraints but its extensions to the non-holonomic constraints. Conventionally the Lagrange multipliers are solved algebraically and substituted into the dynamic equations (DAE). This paper, on the other hand, proposes a method to derive the ordinary differential equations with respect to the Lagrange multipliers. One can resort the ordinary numerical integration method to solve the Lagrange multipliers as same as to solve the ODE with respect to the system coordinates. Some examples of numerical solution for the mechanical models having holonomic and non-holonomic constraints shows the excellent stability of the constraints, which is superior to the Baumgarte’s stabilizing method and the penalty method.