Abstract
The fluid dynamical equations of motion for rotating Riemann ellipsoids are presented as a Lax equation, X = [ F, X]. Riemann ellipsoids model rotating galaxies, stars, and atomic nuclei. The elements of the Lax pair X- F are matrices in the symplectic Lie algebra sp(3, R). The matrix X is formed from the inertia and virial momentum tensors; F is composed from the potential energy, angular velocity, and pressure tensors. The Kelvin circulation is conserved by the Lax system. Riemann ellipsoidal solutions are given by symplectic isospectral deformations.
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