Energy-conserving integration of constrained Hamiltonian systems – a comparison of approaches

Abstract

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.