= Dissipative spreading of a planetary ring
In a <Keplerian shearing sheet>, an <epicyclic guiding center> $x_0$ carries rotating-frame energy $-3\Omega^2x_0^2/8$, plus nonnegative radial and vertical oscillation energies. <Inelastic collisions> dissipate the total <Jacobi energy in a shearing sheet>, while <momentum conservation> preserves $\sum x_0$. Thus $\sum x_0^2$ must grow: the ring spreads about its fixed mean radius. The effect is an <angular momentum transport> process, with some particles moving inward and others outward.
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