Displaying similar documents to “Solving non-holonomic Lagrangian dynamics in terms of almost product structures.”

Non-holonomic mechanical systems in jet bundles.

Manuel de León, David Martín de Diego (1996)

Extracta Mathematicae

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In this paper we present a geometrical formulation for Lagrangian systems subjected to non-holonomic constraints in terms of jet bundles. Cosymplectic geometry and almost product structures are used to obtained the constrained dynamics without using Lagrange multipliers method.

Geometric mechanics on nonholonomic submanifolds

Olga Krupková (2010)

Communications in Mathematics

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In this survey article, nonholonomic mechanics is presented as a part of geometric mechanics. We follow a geometric setting where the constraint manifold is a submanifold in a jet bundle, and a nonholonomic system is modelled as an exterior differential system on the constraint manifold. The approach admits to apply coordinate independent methods, and is not limited to Lagrangian systems under linear constraints. The new methods apply to general (possibly nonconservative) mechanical...

A geometric analysis of dynamical systems with singular Lagrangians

Monika Havelková (2011)

Communications in Mathematics

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We study dynamics of singular Lagrangian systems described by implicit differential equations from a geometric point of view using the exterior differential systems approach. We analyze a concrete Lagrangian previously studied by other authors by methods of Dirac’s constraint theory, and find its complete dynamics.

Conservation laws and symmetry in economic growth models: a geometrical approach.

Manuel de León, David Martín de Diego (1998)

Extracta Mathematicae

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The aim of the present paper is twofold. On one hand, we present a classification of infinitesimal symmetries for Lagrangian systems, and the corresponding Noether theorems. The derivation of the result is made by using the symplectic techniques. Some of the results were previously obtained by other authors (see Prince (1985) for instance), and an exhaustive presentation can be found in de León and Martín de Diego (1995, 1996). Let us note that these results are true even if the Lagrangian...