The GGL variational principle for constrained mechanical systems

Abstract

AbstractWe present an extension of the Livens variational principle (sometimes also referred to as Hamilton-Pontryagin principle) to mechanical systems subject to holonomic constraints. The newly proposed principle embodies an index reduction in the spirit of the often-applied GGL stabilization and thus may be termed “GGL principle”. The Euler-Lagrange equations of the GGL principle assume the form of differential-algebraic equations (DAEs) with differentiation index two. In contrast to the original GGL-DAEs, the present formulation fits into the Hamiltonian framework of mechanics. Therefore, the GGL principle facilitates the design of structure-preserving integrators. In particular, it offers the possibility to construct variational integrators. This is illustrated with the development of a new first-order scheme which is symplectic by design. The numerical properties of the newly devised scheme are investigated for representative examples of constrained mechanical systems.