Noether’s theorem, time-dependent invariants and nonlinear equations of motion

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Abstract
Noether’s theorem is applied to a Lagrangian for a system with nonlinear equations of motion. Noether’s theorem leads to a time‐dependent constant of the motion along with an auxiliary equation of motion. Special cases of this invariant have been used to quantize the time‐dependent harmonic oscillator. We also discuss the solution of the original equations of motion in terms of the solutions to the auxiliary equation.