Lagrangians Galore

Searching for a Lagrangian may seem either a trivial endeavour or an impossible task. In this paper we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H Goldstein, {\it Classical Mechanics}, 2nd edition (Addison-Wesley, Reading, 1980)] and the damped harmonic oscillator. This is the first paper in a series dedicated to this subject.

💡 Research Summary

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The paper entitled “Lagrangians Galore” investigates a systematic way to generate a multitude of Lagrangians for simple classical‑mechanics models by exploiting the Jacobi last multiplier (JLM) together with Lie symmetries. The authors begin by recalling that for a second‑order ordinary differential equation
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