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Multidimensional Euler-Poincaré equations

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Castrillón López, Marco and García Pérez, P.L. (2001) Multidimensional Euler-Poincaré equations. In Differential geometry and its applications. Mathematical Publications (3). Silesian University at Opava, Opava, pp. 383-391. ISBN 80-7248-166-5



Abstract

This work is devoted to presenting a summary of results developed mainly by the first author, T. S. Ratiu and S. Shkoller in their previous work [Proc. Amer. Math. Soc. 128 (2000), no. 7, 2155–2164;].
The main results concern the reduction of a Lagrangian field theory under a group of symmetries, obtaining the analog of the Euler-Poincaré equations, which are also proved to be equivalent to a Noether conservation law given by the symmetry. Furthermore, the compatibility condition needed for obtaining solutions of the original variational problem starting from the solutions of the reduced system is also stated. A final example is given.
The paper is written in geometrical language.


Item Type:Book Section
Additional Information:

Proceedings of the 8th International Conference held in Opava, August 27–31, 2001.

Uncontrolled Keywords:Lagrangian formalism and Hamiltonian formalism
Subjects:Sciences > Mathematics > Algebraic geometry
Sciences > Mathematics > Topology
ID Code:23937
Deposited On:13 Dec 2013 18:28
Last Modified:12 Dec 2018 15:13

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