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Are normal modes the eigenvectors of the matrix $(\omega ^2 T- V)$ where $T$ is the matrix of kinetic energy and $V$ is the matrix of potential energy?

Is it the only way to express them?

How can I express them using the coordinates that I have choosen at the beginning of the exercise?

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$V$ will be the matrix of the derivatives of the potential energy. – Pricklebush Tickletush Dec 22 '12 at 17:38
@AlecS V is the matrix of coefficients of the coordinates and near the position of equilibrium it can be approximated to hessian matrix of the potential energy... are we saying the same thing? – sunrise Dec 22 '12 at 18:42
Yeah, we are saying the same thing. – Pricklebush Tickletush Dec 22 '12 at 21:27
@user1104 Could you help me? – sunrise Dec 30 '12 at 7:25
Could you give me a little more context? – Pricklebush Tickletush Dec 30 '12 at 19:35

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