Modeling of Dirac Dynamical Systems and its Discrete Variational Formulation

Abstract

In this paper, we develop a variational discretization of Lagrangian systems based on the Lagrange-d’Alembert-Pontryagin principle, which is equivalent with the nonholonomic integrator based on the Lagrange-d’Alembert principle. In particular, we show there exist (±)- formulas which have been unknown for the obtained discrete Lagrange-d’Alembert equations and we also clarify the intrinsic expression of the discrete Lagrange-d’Alembert-Pontryagin principle.