Beginning at 31:03 Dr. Susskind presents an intuitively very satisfying derivation of the Euler-La Grange equation(s). But, I'm not convinced it is rigorous. It seems his choice of variation is not the only possible choice for the neighborhood he selected.(adsbygoogle = window.adsbygoogle || []).push({});

The reason this matters to me is because, in his derivation velocity and position seem to be implicitly coupled. My understanding of the Euler-La Grange equations is that position and velocity are independent variables. Lemons Section 2.2 gives a more abstract and symbolic derivation. I understand that to say that: given any variation in position, there are an infinite number of variations in velocity possible, and vis-versa.

Can these two derivations be shown to be equivalent?

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# Is Susskind's derivation Euler-La Grange rigorous?

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