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

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.

arXiv comment14 pages, to be published in J. Math. Phys

References in corpus (5)

• The geometric origin of Lie point symmetries of the Schrödinger and the Klein Gordon equations
• Symmetry analysis of the Klein-Gordon equation in Bianchi I spacetimes
• Approximate Noether gauge symmetries of Bardeen model
• Lie and Noether point symmetries of a class of quasilinear systems of second-order differential equations
• Noether symmetries and isometries of the minimal surface Lagrangian under constant volume in a Riemannian space

Cited by in corpus (5)

• Constraining Non-local Gravity by S2 star orbits
• New conservation laws and exact cosmological solutions in Brans-Dicke cosmology with an extra scalar field
• Quadratic conservation laws and collineations: a discussion
• Quadratic first integrals of time-dependent dynamical systems of the form ${\ddot{q}}^a=-{\Gamma }_{bc}^a{\dot{q}}^b{\dot{q}}^c-\omega (t)Q^a(q)$
• The Unified Soliton System as the $\mathrm{Ad}{\mathrm{S}}_2$ System