Mechanical presymplectic structures and Marsden-Weinstein reduction of time-dependent Hamiltonian systems

I. Gutierrez-Sagredo; D. Iglesias Ponte; J. C. Marrero; E. Padrón

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arXiv · 2411.11997

Mechanical presymplectic structures and Marsden-Weinstein reduction of time-dependent Hamiltonian systems

I. Gutierrez-Sagredo·D. Iglesias Ponte·J. C. Marrero·E. Padrón

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Abstract

In 1986, Albert proposed a Marsden-Weinstein reduction process for cosymplectic structures. In this paper, we present the limitations of this theory in the application of the reduction of symmetric time-dependent Hamiltonian systems. As a consequence, we conclude that cosymplectic geometry is not appropriate for this reduction. Motived for this fact, we replace cosymplectic structures by more general structures: mechanical presymplectic structures. Then, we develop Marsden-Weinstein reduction for this kind of structures and we apply this theory to interesting examples of time-dependent Hamiltonian systems for which Albert's reduction method doesn't work.

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BibTeX RIS

I. Gutierrez-Sagredo, D. Iglesias Ponte, J. C. Marrero, E. Padrón. 2024-11-18. Mechanical presymplectic structures and Marsden-Weinstein reduction of time-dependent Hamiltonian systems. https://arxiv.org/abs/2411.11997

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