caa a22 4500 445331658 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s10208-011-9096-2 doi (NATIONALLICENCE)springer-10.1007/s10208-011-9096-2 Variational and Geometric Structures of Discrete Dirac Mechanics [Elektronische Daten] [Melvin Leok, Tomoki Ohsawa] In this paper, we develop the theoretical foundations of discrete Dirac mechanics, that is, discrete mechanics of degenerate Lagrangian/Hamiltonian systems with constraints. We first construct discrete analogues of Tulczyjew's triple and induced Dirac structures by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides a means of deriving discrete Lagrange-Dirac and nonholonomic Hamiltonian systems. In particular, this yields nonholonomic Lagrangian and Hamiltonian integrators. We also introduce discrete Lagrange-d'Alembert-Pontryagin and Hamilton-d'Alembert variational principles, which provide an alternative derivation of the same set of integration algorithms. The paper provides a unified treatment of discrete Lagrangian and Hamiltonian mechanics in the more general setting of discrete Dirac mechanics, as well as a generalization of symplectic and Poisson integrators to the broader category of Dirac integrators. SFoCM, 2011 Dirac structures nationallicence Lagrange-Dirac systems nationallicence Geometric integration nationallicence Leok Melvin Department of Mathematics, University of California, 9500 Gilman Drive, La Jolla, San Diego, CA, USA aut Ohsawa Tomoki Department of Mathematics, University of California, 9500 Gilman Drive, La Jolla, San Diego, CA, USA aut Foundations of Computational Mathematics Springer-Verlag 11/5(2011-10-01), 529-562 1615-3375 11:5<529 2011 11 10208 https://doi.org/10.1007/s10208-011-9096-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-011-9096-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Leok Melvin Department of Mathematics, University of California, 9500 Gilman Drive, La Jolla, San Diego, CA, USA aut NATIONALLICENCE 700 1- Ohsawa Tomoki Department of Mathematics, University of California, 9500 Gilman Drive, La Jolla, San Diego, CA, USA aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/5(2011-10-01), 529-562 1615-3375 11:5<529 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer