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arXiv · 2006.14844

Lagrangian dynamics by nonlocal constants of motion

Gianluca Gorni·Gaetano Zampieri
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Abstract

A simple general theorem is used as a tool that generates nonlocal constants of motion for Lagrangian systems. We review some cases where the constants that we find are useful in the study of the systems: the homogeneous potentials of degree~$-2$, the mechanical systems with viscous fluid resistance and the conservative and dissipative Maxwell-Bloch equations of laser dynamics. We also prove a new result on explosion in the past for mechanical system with hydraulic (quadratic) fluid resistance and bounded potential.

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Gianluca Gorni, Gaetano Zampieri. 2020-06-26. Lagrangian dynamics by nonlocal constants of motion. https://doi.org/10.3934/dcdss.2020216

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