SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Variational Integrators and Discrete Lagrangian Mechanics for Interconnected Systems

H. Yoshimura and S. Hanawa

Abstract
It has been focused upon developing stable and efficient numerical integrators for large scale systems such as electric networks and multibody space structures. In particular, it is no doubt that the structure-preserving or variational integrators must be an essential tool for design and analysis of nonconservative as well as conservative interconnected systems, where the interconnection may be given by constraints (see [1, 2]). In this talk, we explore variational integrators for interconnected systems with degenerate Lagrangians, where the degeneracy may induce the primary constraints in the sense of Dirac in addition to holonomic constraints. We show the discrete variational structures for holonomic Lagrangian systems for electric transmission lines by interconnecting modular electric circuits. We also show numerical validity of our theory in comparison with conventional integrators for constrained Lagrangian systems.

Bibliography
[1] H. Yoshimura and J. E. Marsden, Dirac structures and implicit Lagrangian systems in electric networks, Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems, Paper WeA08.5, 2006, pp.1-6.
[2] H. Yoshimura and A. Yoshida, Discrete constrained Lagrangian systems and geometric constraint stabilization, Proceedings of the 8th International Conference of Numerical Analysis and Applied Mathematics, 2010, pp.1292-1295.

Organized by         Universidad de Valladolid     IMUVA