A Decoupling Solution Method for Implicit Numerical Integration of Constrained Mechanical Systems*

Abstract

A decoupling solution method is presented for implicit numerical integration of constrained multibody systems. Compared to implicit numerical integration methods, explicit numerical integration methods usually spend less computation time per iteration, since the equations of motion and an explicit integration formula coupled with the constraint manifolds are solved separately. However, the integration step size can be excessively small for highly nonlinear or stiff problems, due to the small stability region of the explicit method. In contrast, implicit numerical integration methods do not have the problem of excessive small step size. Implicit integration methods, however, generally require one to solve a large system equations simultaneously. The solution method proposed in this paper eliminates the problem of large system equations, while maintaining the advantage of the implicit method. Furthermore, the proposed method provides a well-conditioned iteration matrix for the implicit method, which is important to obtain accurate and stable solutions.