Driven damped nth-power anharmonic oscillators with time-dependent coefficients and their integrals of motion

Abstract

In this manuscript, we derive integrals of motion for general anharmonic oscillators with damping and power-law forcing. The model under investigation has time-dependent coefficients, and the determination of these physical quantities is carried out using Noether´s theorem. The solutions must satisfy appropriate analytical conditions for the proposed quantities to be true integrals of motion. In turn, these analytical conditions are associated to well know physical systems, including the Milne-Pinney and Ermakov-Lewis models. We provide various numerical solutions of our equations of motion and the associated integrals to verify the theoretical results.