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.

14 pages, to be published in J. Math. Phys

References in corpus (3)

• Symmetry analysis of the Klein-Gordon equation in Bianchi I spacetimes
• Approximate Noether gauge symmetries of Bardeen model
• Noether symmetries and isometries of the minimal surface Lagrangian under constant volume in a Riemannian space

Cited by in corpus (1)

• Quadratic first integrals of time-dependent dynamical systems of the form ${\ddot{q}}^a=-{\Gamma }_{bc}^a{\dot{q}}^b{\dot{q}}^c-\omega (t)Q^a(q)$