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 computing system accelerations from given force functions and constraints and (ii) the numerical integration problem for advancing the state in time. For the forward dynamics problem, algorithms have been given with optimal, linear complexity in the number of bodies, in case the system topology does not contain many closed loops. But the interaction between these two stages can be important. Using explicit time integration schemes, we propose a sequential regularization method (SRM) that has a linear complexity in the number of bodies per time step, even in the presence of many closed loops. The method also handles certain types of constraint singularity.