Numerical Solution of

One of the outstanding problems in the numerical simulation of mechanical systems is the development of eecient methods for dealing with highly oscilla-tory systems. These types of systems arise for example in vehicle simulation in modeling the suspension system or tires, in models for contact and impact, in exible body simulation from vibrations in the structural model, and in molecular dynamics. Simulations involving high frequency vibration can take a huge number of time steps, often as a consequence of oscillations which are not physically important. The components causing the oscillations cannot usually be eliminated from the model because in some situations they are critical to the simulation. The equations of motion of a multibody mechanical system are described by a system of diierential-algebraic equations (DAEs). In this paper, we will explore two types of methods. The rst class of methods damps out the oscillation via highly stable implicit methods. Even in this relatively simple approach , unforseen problems may arise for Newton iteration convergence, due to the nonlinearities. The second class of methods involves linearizing the system around the smooth solution. The linearized system can be solved rapidly via a number of diierent methods. the content of which does not necessarily reeect the position or the policy of the government, and no oocial endorsement should be inferred.