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Variational integrators for interconnected Lagrange-Dirac systems. (English) Zbl 1378.37113

Summary: 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 [H. O. Jacobs and H. Yoshimura, J. Geom. Mech. 6, No. 1, 67–98 (2014; Zbl 1304.70016)] and discrete Dirac variational integrators [M. Leok and T. Ohsawa, Found. Comput. Math. 11, No. 5, 529–562 (2011; Zbl 1231.70016)]. We test our results by simulating some of the continuous examples given in [H. O. Jacobs and H. Yoshimura, J. Geom. Mech. 6, No. 1, 67–98 (2014; Zbl 1304.70016)].

MSC:

37J60 Nonholonomic dynamical systems
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
37N05 Dynamical systems in classical and celestial mechanics
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
70F25 Nonholonomic systems related to the dynamics of a system of particles
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70H05 Hamilton’s equations
70H45 Constrained dynamics, Dirac’s theory of constraints
70Q05 Control of mechanical systems
93A30 Mathematical modelling of systems (MSC2010)
93B27 Geometric methods
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References:

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