Variational and Geometric Structures of Discrete Dirac Mechanics
نویسندگان
چکیده
منابع مشابه
Variational and Geometric Structures of Discrete Dirac Mechanics
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 ...
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We construct discrete analogues of Dirac structures by considering the geometry of symplectic maps and their associated generating functions, in a manner analogous to the construction of continuous Dirac structures in terms of the geometry of symplectic vector fields and their associated Hamiltonians. We demonstrate that this framework provides a means of deriving implicit discrete Lagrangian a...
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We 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 implicit discrete Lagrangian and Hamiltonian systems, while incorporating discrete Dirac constraints. In particular, this yields implicit nonholonomic Lagrangia...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2011
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-011-9096-2