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 known 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.

在本手稿中，我们推导了具有阻尼和幂律强迫的一般非谐振荡器的运动积分。所研究的模型具有随时间变化的系数，这些物理量的确定是使用Noether定理进行的。解决方案必须满足适当的分析条件，才能使建议的数量成为运动的真实积分。反过来，这些分析条件与众所周知的物理系统相关，包括Milne-Pinney和Ermakov-Lewis模型。我们提供运动方程和相关积分的各种数值解，以验证理论结果。