Lie and Noether point symmetries for a class of nonautonomous dynamical systems

摘要

We prove two general theorems that determine the Lie and the Noether point symmetries for the equations of motion of a dynamical system thatmoves 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. Published by AIP Publishing.