Mass-weighted coordinate
= Mass-weighted coordinate
{title2=$q_i=\sqrt{m_i}\,x_i$}
For diagonal kinetic energy, $q_i=\sqrt{m_i}\,x_i$ changes the kinetic quadratic form to $\tfrac12\sum_i\dot q_i^2$. The potential Hessian in these coordinates is $M^{-1/2}KM^{-1/2}$.