= Mass-weighted elastic normal modes
{title2=$\hat H\mathbf u_\alpha=\rho\omega_\alpha^2\mathbf u_\alpha$}
For a conservative elastic body, the stiffness operator is a <self-adjoint operator> under compatible <boundary conditions>. The dynamical operator $\rho^{-1}\hat H$ is self-adjoint in the mass <inner product> $\langle\mathbf u,\mathbf v\rangle_\rho=\int\rho\mathbf u^*\cdot\mathbf v\,dV$. Choosing mass-normalized <normal modes> converts the field equation into independent forced oscillators. If the <normal modes> have mass norm $N_\alpha$ instead, each projected force must be divided by $N_\alpha$.
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