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As some background, this question came from a throwaway exercise by my professor for a reminder of Lagrangian mechanics in a relativistic setting. The original exercise simply gave the Lagrangian and asked us to compute the equation of motion. This piqued my interest since it can be motivated as described in my question.

It would seem at least reasonable to me if the question was closed as duplicate or low-effort, in which case I could supply some more details. But it's surprising for it to be closed as non-mainstream physics. Now of course the Lagrangian is not intended to be a model of some real system, since it's just a toy system that's easy to compute with. Nor am I asking for the correctness of any personal theories. It is instead asking for pointers to literature studying a specific physical system. Should this question be reopened?

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  • $\begingroup$ The question was re-opened. $\endgroup$ Commented Aug 28 at 14:33

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I voted to close as “non-mainstream” ‘cuz I couldn’t find anything better at the time. Statements such as “Consider this alternative model” and “Has this toy model, or any close variations, been studied in the literature” are not good for the format of this site. It doesn’t help to claim as above that the “Lagrangian is not intended to be a model for a real system”.

The first statement is speculative and borderline non-mainstream: you did not do a good job of explaining the physics behind you assumption, and it’s not clear why your assumption $A_\mu \dot{x}^{\mu}=0$ should make sense, or what problem you’re trying to solve. Statements like “in some sense” are vague and it’s really your job to clearly specify in what precise sense $g$ is proportional to the moment of inertia. I could go on.

The second has an simple no/yes answer.

As a result, I don’t know how your question can be answered using common physics principles.

I quite possibly choose the wrong reason to close but your question right now lacks clarity and should be closed as such. Thankfully for you I don’t have another close vote for your question.

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