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[tex] \frac{d}{dt} \frac{\partial \cal L}{\partial \dot{q}} - \frac{\partial \cal L}{\partial q} = 0[/tex]

with little algebra directly from Hamilton's principle, like the geometric derivation of snell's law from the principle of least time. It should be possible since they're simple enough to write. I've tried for about an hour with little luck. Does any one know how to do it?