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arXiv · 1708.00619

Lie and Noether point Symmetries for a Class of Nonautonomous Dynamical Systems

Leonidas Karpathopoulos·Andronikos Paliathanasis·Michael Tsamparlis
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Abstract

We prove two general theorems which determine the Lie and the Noether point symmetries for the equations of motion of a dynamical system which moves in a general Riemannian space under the action of a time dependent potential $W(t,x)=\omega(t)V(x)$. We apply the theorems to the case of a time dependent central potential and the harmonic oscillator and determine all Lie and Noether point symmetries. Finally we prove that these theorems also apply to the case of a dynamical system with linear dumping and study two examples.

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BibTeXRIS

Leonidas Karpathopoulos, Andronikos Paliathanasis, Michael Tsamparlis. 2017-08-02. Lie and Noether point Symmetries for a Class of Nonautonomous Dynamical Systems. https://doi.org/10.1063/1.4998715

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