A structure preserving approach to the simulation of non-smooth dynamics

The investigated multibody dynamics involve perfectly elastic, partially elastic and perfectly plastic contacts and a structure preserving approach is used in forward dynamics and optimal control simulations. The applied mechanical integrator is based on a constrained version of the Lagrange-d’Alembert principle and it represents exactly the behaviour of the analytical solution concerning the consistency of momentum maps and symplecticity: it is called symplectic momentum scheme. To guarantee the geometric exactness during the establishing or releasing of contacts, the non-smooth problem is solved including the computation of the contact configuration, time and force, instead of relying on a smooth approximation of the contact problem via a penalty potential. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)