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arXiv · 1402.2847

Reduced dynamics and Lagrangian submanifolds of symplectic manifolds

E. García-Toraño Andrés·E. Guzmán·J. C. Marrero·T. Mestdag
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Abstract

In this paper, we will see that the symplectic creed by Weinstein "everything is a Lagrangian submanifold" also holds for Hamilton-Poincar\'e and Lagrange-Poincar\'e reduction. In fact, we show that solutions of the Hamilton-Poincar\'e equations and of the Lagrange-Poincar\'e equations are in one-to-one correspondence with distinguished curves in a Lagrangian submanifold of a symplectic manifold. For this purpose, we will combine the concept of a Tulczyjew triple with Marsden-Weinstein symplectic reduction.

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BibTeXRIS

E. García-Toraño Andrés, E. Guzmán, J. C. Marrero, T. Mestdag. 2014-02-12. Reduced dynamics and Lagrangian submanifolds of symplectic manifolds. https://doi.org/10.1088/1751-8113/47/22/225203

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