A Mathematical Corrector Method of Constrained Dynamic Systems

Abstract

This paper presents a numerical corrector method to find feasible state variables of the constrained multibody systems. For correcting state variables, the Lagrange-Newton method, a nonlinear optimization technique, is used. The iteration formulae derived from the quasi-Newton scheme do not update the Lagrange multipliers in the analysis steps and projects the state variables on the constraint manifold. Therefore, the cost due to the updating of Lagrange multipliers decreases. The method is verified through the convergence theorem denoting a convergence order of numerical solutions and as the corrections are performed along the constraint gradients, the system motion is formed in the null space tangent to the constraint manifold. The simulation example uses a three-dimensional full vehicle model, and the obtained numerical solutions are compared with the ADAMS solutions.