Assuming I've understood some claims correctly, having defined the canonical momenta with equation(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

p_k = \frac{\partial L}{\partial \dot{q}_k},

[/tex]

we can solve the velocities as functions

[tex]

\dot{q}_k(q_1,\ldots,q_n,p_1,\ldots, p_n)

[/tex]

precisely when the determinant

[tex]

\textrm{det}\Big(\Big(\frac{\partial^2 L}{\partial \dot{q}_k\partial\dot{q}_{k'}}\Big)_{k,k'\in\{1,\ldots,n\}}\Big)

[/tex]

is non-zero. Why is this the case? The result looks reasonable, but I have difficulty seeing where this is coming from.

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# Velocities as function of canonical momenta

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