On the Damped Pinney Equation from Noether Symmetry Principles
Classical Physics
2024-10-10 v1
Abstract
There are several versions of the damped form of the celebrated Pinney equation, which is the natural partner of the undamped time-dependent harmonic oscillator. In this work these dissipative versions of the Pinney equation are briefly reviewed. We show that Noether's theorem for the usual time-dependent harmonic oscillator as a guiding principle for derivation of the Pinney equation also works in the damped case, selecting a Noether symmetry based damped Pinney equation. The results are extended to general nonlinear damped Ermakov systems. A certain time-rescaling always allows to remove the damping from the final equations.
Cite
@article{arxiv.2410.06350,
title = {On the Damped Pinney Equation from Noether Symmetry Principles},
author = {Fernando Haas},
journal= {arXiv preprint arXiv:2410.06350},
year = {2024}
}