Quasistatic approximations for stiff second order differential equations

摘要

Stiff terms in second order ordinary differential equations may cause large computation time due to high frequency oscillations. Quasistatic approximations eliminate these high frequency solution components in the dynamical simulation of multibody systems by neglecting inertia forces. In the present paper, we study the approximation error of this approach using classical results from singular perturbation theory. The transformation of the linearly implicit second order model equations from multibody dynamics to the canonical (semi-)explicit form of first order singularly perturbed ordinary differential equations is studied in detail. Numerical tests for the model of a walking mobile robot with stiff contact forces between legs and ground show that the computation time may be reduced by a factor up to 10 using the proposed quasistatic approximation.