= Spring model of magnetorotational instability
For an incompressible vertical-field mode, frozen-in <magnetic tension> supplies a spring of frequency $\omega_A$. Its displacement satisfies $\ddot\xi_x-2\Omega\dot\xi_y-4\Omega A\xi_x=-\omega_A^2\xi_x$ and $\ddot\xi_y+2\Omega\dot\xi_x=-\omega_A^2\xi_y$. Their <determinant> gives the <ideal magnetorotational dispersion relation>. A weak spring transfers <angular momentum> from the faster inner element to the slower outer element, causing inward and outward migration that increase their separation when angular velocity decreases outward. A sufficiently strong spring instead supplies a restoring force.
// Target: physics.bigb
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