Classical Dynamical Symmetries and Geometry of Trajectories

Christian Carimalo

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arXiv · 2401.17021

Classical Dynamical Symmetries and Geometry of Trajectories

Christian Carimalo

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Abstract

It is shown that all spherical symmetric potentials are capable of producing dynamical symmetries in classical one-body motions, thanks to the inevitable existence of symmetry axes associated with turning points for corresponding trajectories. This will definitely expand the class of maximally superintegrable one-body motions in central potentials that until now was considered to include only the Newtonian and Hookean cases. A simple method is proposed to identify and characterize these dynamical symmetries.

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Christian Carimalo. 2024-01-30. Classical Dynamical Symmetries and Geometry of Trajectories. https://arxiv.org/abs/2401.17021

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