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 dynam- ics. We also prove a new result on explosion in the past for mechanical system with hydraulic (quadratic) fluid resistance and bounded potential.
Lagrangian dynamics by nonlocal constants of motion
Zampieri, Gaetano
Membro del Collaboration Group
2020-01-01
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 dynam- ics. 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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