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Variational Integrators for Interconnected Lagrange–Dirac Systems

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Abstract

Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange–Dirac mechanical systems provide a broad category of mathematical models that are closed under interconnection, and in this paper, we develop a framework for the interconnection of discrete Lagrange–Dirac mechanical systems, with a view toward constructing geometric structure-preserving discretizations of interconnected systems. This work builds on previous work on the interconnection of continuous Lagrange–Dirac systems (Jacobs and Yoshimura in J Geom Mech 6(1):67–98, 2014) and discrete Dirac variational integrators (Leok and Ohsawa in Found Comput Math 11(5), 529–562, 2011). We test our results by simulating some of the continuous examples given in Jacobs and Yoshimura (2014).

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Acknowledgements

We gratefully acknowledge helpful comments and suggestions of the referee. HP has been supported by the NSF Graduate Research Fellowship Grant Number DGE-1144086. ML has been supported in part by NSF under Grants DMS-1010687, CMMI-1029445, DMS-1065972, CMMI-1334759, DMS-1411792, DMS-1345013.

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  1. Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, USA

    Helen Parks & Melvin Leok

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  1. Helen Parks
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  2. Melvin Leok
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Correspondence to Melvin Leok.

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Communicated by Anthony Bloch.

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Parks, H., Leok, M. Variational Integrators for Interconnected Lagrange–Dirac Systems. J Nonlinear Sci 27, 1399–1434 (2017). https://doi.org/10.1007/s00332-017-9364-7

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