Structure‐preserving integrators for constrained mechanical systems in the framework of the GGL principle

Simulating multi-body systems often requires an appropriate treatment of the differential-algebraic equations (DAEs). The recently proposed GGL principle considers constraints both on configuration and on velocity level and embodies an index-reduction technique in the spirit of the often-applied GGL stabilization. In sharp contrast to the original formulation, the Euler-Lagrange equations of the GGL principle, fit into the Hamiltonian framework of mechanics. Therefore, the GGL principle facilitates the design of structure-preserving integrators. Due to the close relationship of the GGL principle to optimal control, previously developed direct methods can be used to obtain variational integrators for constrained mechanical systems. Furthermore, slight modifications can be applied to obtain second-order energy-momentum consistent integrators emanating from the GGL principle, which represent another important class of structure-preserving time-stepping schemes. The newly devised schemes circumvent issues of standard methods and provide more realistic results by accounting for velocity level constraints.