I have a Lagrangian [tex]L = \frac{R^2}{z^2} ( -\dot{t}^2 +\dot{x}^2 +\dot{y}^2 +\dot{z}^2)[/tex] and I want to find the Euler-Lagrange equations [tex]\frac{\partial L}{\partial q} = \frac{d}{ds} \frac{\partial L}{\partial \dot{q}}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

I'm fine with the LHS and the partial differentiation on the RHS, but when it comes to the [tex]\frac{d}{ds} [/tex] I'm not sure which coordinates I'm supposed to consider as a function of s.

Is it all of them (ie t, x, y, z, and their derivatives)

Or is it only the one I'm doing the equation for (so for the z-equation that's just z and its derivative)?

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# Euler-Lagrange eqns confusion

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