An Efficient Newton-Type Iteration for the Numerical Solution of Highly Oscillatory Constrained Multibody Dynamic Systems

In this paper we present a coordinate-split (CS) technique for the numerical solution of the equations of motion of constrained multibody dynamic systems. We show how the coordinate-split technique can be implemented within the context of commonly used solution methods, for increased eeciency and reliability. A particularly challenging problem for multibody dynamics is the numerical solution of highly oscillatory nonlinear mechanical systems. Highly stable implicit integration methods with large stepsizes can be used to damp the oscillation , if it is of small amplitude. However, the standard Newton iteration is known to experience severe convergence diiculties which force a restriction of the stepsize. We introduce a modiied coordinate-split (CM) iteration which overcomes these problems. Convergence analysis explains the improved convergence for nonlinear oscillatory systems, and numerical experiments illustrate the eeectiveness of the new method.