= Singular kinetic matrix in small oscillations
{title2=$\mathsf M\ddot q+\mathsf Kq=0,\quad\det\mathsf M=0$}
If the quadratic <kinetic energy> has a singular coefficient matrix, some <generalized coordinates> have no independent linearized inertia. The <small oscillation> equations can then contain algebraic constraints, and the number of finite <normal mode> frequencies can be smaller than the number of coordinates. One should use the polynomial $\det(\mathsf K-\omega^2\mathsf M)$ without dividing by $\det\mathsf M$. Giving a nominally massless component a small mass can restore a high-frequency mode whose frequency diverges as that mass tends to zero.
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