On the Stability of Differentially Rotating Bodies

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Abstract
A variational principle of great power is derived. It is naturally adapted for computers, and may be used to determine the stability of any fluid flow including those in differentially-rotating, self-gravitating stars and galaxies. The method also provides a powerful theoretical tool for studying general properties of eigen-functions, and the relationships between secular and ordinary stability. In particular we prove the anti-spiral theorem indicating that no stable (or steady) mode can have a spiral structure.

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