Sequential regularization methods for simulating mechanical systems with many closed loops

The numerical simulation problem of large multibody systems has often been treated in two separate stages: (i) the forward dynamics problem for comput ing system accelerations from given force functions and constraints and (ii ) the numerical integration problem for advancing the state in time. For th e forward dynamics problem, algorithms have been given with optimal, linear complexity in the number of bodies, in case the system topology does not c ontain many closed loops. But the interaction between these two stages can be important. Using explic it time integration schemes, we propose a sequential regularization method (SRM) that has a linear complexity in the number of bodies per time step, e ven in the presence of many closed loops. The method also handles certain t ypes of constraint singularity.