(adsbygoogle = window.adsbygoogle || []).push({}); Lagrangian Mass Matrix Question, Pls Help!!

"Assume that the lagrangian is given in the form

[tex] L(q_{i}, q_{i}', t) = \sum_{m, n}T_{mn}(q_{i})q_{m}'q_{n}' - V(q_{i})[/tex]

Show that in order for the principle of least action to hold, [tex]T_{mn}(q_{i})[/tex] has to be positive definite."

My first intuition is that T has to be positive definite so that the action will be a minimum. However, when I tried to expand the lagragian to the second order, it gets kind of messy and I cannot find a way to eliminate. It is kind of urgent and I hope those who know will kindly help.

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# Homework Help: Lagrangian Mass Matrix Question, Pls Help

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