I can't find the math of that.

Imagine a vibrating object, like a circular membrane, with vibration modes $\phi_{ij}(x,y)$. Let's express the initial vibration state like

$u(x,y,t)=\sum_{ij}a_{ij}e^{i\omega_{ij} t}\phi_{ij}(x,y)$

Now imagine that this membrane is physically rotated by an angle $\theta$ while vibrating. What becomes the vibration state? In other words, what become the different $a_{ij}$?

If the membrane is initially vibrating with some privileged direction, this direction must be conserved with respect to an inertial frame of reference, by analogy with the Foucault effect. So the $a_{ij}$ should change but how?

Thanks a lot!


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