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SUMMARY The objective of the present work is to formulate a new class of discontinuous variational time integrators that allow the system to adopt two possibly different configurations at each sampling time t k, representing predictor and corrector configurations of the system. The resulting sequence of configuration pairs then represents a discontinuous-or non-classical-trajectory. Continuous or classical trajectories are recovered simply by enforcing a continuity constraint at all times. In particular, in systems subject to one-sided contact constraints simulated via discontinuous variational time integrators, the predictor configuration is not required to satisfy the one-sided constraints, whereas the corrector configuration is obtained by a closest-point projection (CPP) onto the admissible set. The resulting trajectories are generally discontinuous, or non-classical, but are expected to converge to classical or continuous solutions for decreasing time steps. We account for dissipation, including friction, by means of a discrete Lagrange-d'Alembert principle, and make extensive use of the spacetime formalism in order to ensure exact energy conservation in conservative systems, and the right rate of energy decay in dissipative systems. The structure, range and scope of the discontinuous variational time integrators, and their accuracy characteristics are illustrated by means of examples of application concerned with rigid multibody dynamics. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper known results for continuous Hamiltonian systems subject to holonomic constraints are carried over to a special class of discrete systems, namely to discrete Hamiltonian systems in the sense of Gonzalez [6]. In particular the equivalence of the Lagrange Multiplier Method to the Penalty Method (in the limit for increasing penalty parameters) and to the Augmented Lagrange Method (for infinitely many iterations) is shown theoretically. In doing so many features of the different systems, including dimension, condition number, accuracy, etc. are discussed and compared. Two numerical examples are dealt with to illustrate the results. [ABSTRACT FROM AUTHOR]