Integration of strongly damped mechanical systems by Runge-Kutta methods

Strongly damped mechanical systems arise, for example, in vehicle dynamics and in modelling joints in biomechanics. Standard explicit integrators become unstable unless very small time steps are chosen. We are interested in the numerical solution of such systems with step sizes that are independent of the damping parameter. The smooth motion of the mechanical system is expanded in terms of solutions of differential-algebraic systems of index 2. These results hold for analytical solutions as well as for numerical solutions of suitable methods such as Radau collocation. In the border case of big damping constants it turns out that the error of numerical solutions of the strongly damped mechanical system is bounded by errors for the differential algebraic systems.