Dirac structures in Lagrangian mechanics Part I: Implicit Lagrangian systems
نویسندگان
چکیده
منابع مشابه
Dirac Structures in Lagrangian Mechanics Part I: Implicit Lagrangian Systems
This paper develops the notion of implicit Lagrangian systems and presents some of their basic properties in the context of Dirac structures. This setting includes degenerate Lagrangian systems and systems with both holonomic and nonholonomic constraints, as well as networks of Lagrangian mechanical systems. The definition of implicit Lagrangian systems with a configuration space Q makes use of...
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Part I of this paper introduced the notion of implicit Lagrangian systems and their geometric structure was explored in the context of Dirac structures. In this part, we develop the variational structure of implicit Lagrangian systems. Specifically, we show that the implicit Euler-Lagrange equations can be formulated using an extended variational principle of Hamilton called the Hamilton-Pontry...
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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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The idea of multiport systems has been known as a useful tool when regarding a system as an interconnection of physical elements throughout principle of power invariance, which has been widely used in electrical circuits and networks (see, for instance, [4, 14]), where the principle of power invariance is known as Tellegen’s theorem in electrical network theory (see [6]). From the viewpoint of ...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2006
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2006.02.009