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For questions involving the Lagrangian formulation of a dynamical system. Namely, the application of an action principle to a suitably chosen Lagrangian or Lagrangian Density in order to obtain the equations of motion of the system.

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Equation of Motion Invariance in Galilean Mechanics

Consider a particle moving freely, where $\vec{r}(t)$ is the position of the particle. Suppose I move into a frame with $$\vec{r}' =\vec{r} + \epsilon \vec{F}(\vec{r}, t)\tag{1},$$ where $\epsilon$ i …
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Equation of Motion Invariance in Galilean Mechanics

Thank you for the great responses, this makes way more sense to me now. I also want to add my understanding of the answers and a clarification of the subtlety that confused me initially. It is a mathe …
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