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

2024/11/18 by I. Gutierrez-Sagredo, David Iglesias Ponte, Gutierrez-Sagredo, I. +5 · 1 citation
Engineering · #53D20 #70G45 #70G65 #70H05 #70H33 #Control and Stability of Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2411.11997

openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Hamiltonian reduction from particular integrals

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