A recursive multibody formalism for systems with small mass and inertia terms

Abstract. Complex multibody system models that contain bodies with small mass or nearly singular inertia tensor may suffer from high frequency solution components that deteriorate the solver efficiency in time integration. Singular perturbation theory suggests to neglect these small mass and inertia terms to allow a more efficient computation of the smooth solution components. In the present paper, a recursive multibody formalism is developed to evaluate the equations of motion for a tree structured N body system with O(N) complexity even if isolated bodies have a rank-deficient body mass matrix. The approach is illustrated by some academic test problems in 2-D.