RUNGE-KUTTA INTEGRATORS FOR MULTIBODY DYNAMICS

The governing equations of multibody dynamics are mixed differential-a lgebraic equations (DAEs) of index three, which precludes direct use o f most numerical integrators. In the present paper local parameterizat ions of the manifold defined by the algebraic equations are used to re duce the DAE locally to a state-space form (SSF), which is an ordinary differential equation (ODE) of dimension equal to the number of degre es of freedom. It is then shown that a numerical solution of the origi nal DAE that corresponds to a Runge-Kutta solution of the local SSF ca n be obtained at a cost of only one factorization of a symmetric matri x per integration step.