BDF integrators for constrained mechanical systems on Lie groups

Multistep methods of BDF type are the method-of-choice in several industrial multibody system simulation packages. In the present paper, BDF is applied to constrained systems in nonlinear configuration spaces with Lie group structure that allows, e.g., a representation of multibody systems with large rotations without singularities. The k-step Lie group integrator BLieDF avoids order reduction by a slightly perturbed argument of the exponential map for representing the nonlinearity of the numerical flow in the configuration space without any time-consuming re-parametrization. This integrator is compared with multistep methods on Lie groups suggested by Faltinsen, Marthinsen and Munthe-Kaas (2001) and the advantages of the novel BLieDF integrator are shown. (C) 2019 Published by Elsevier B.V.

Automated summary

In this paper, BDF type multistep methods were applied to constrained systems with Lie group structure. The k-step Lie group integrator BLieDF, which avoids order reduction by perturbing the argument of the exponential map, was compared with multistep methods on Lie groups suggested by Faltinsen, Marthinsen and Munthe-Kaas, showing its advantages.