Abstract
This chapter discusses the Hamiltonian dynamics of Riemann ellipsoids. The classical theory of Riemann ellipsoids is a Hamiltonian dynamical system defined on the co-adjoint orbits of the Lie group. A Riemann ellipsoid is a fluid with an ellipsoidal boundary whose motion is constrained to an orbit of the kinematical group. Each Riemann ellipsoid phase space is a symplectic manifold on which the Lie group cm(3) acts transitively as a group of canonical transformations. The application of Lie groups in classical mechanics has been restricted heretofore to symmetry groups for which the group action commutes with the flow. In contrast, cm(3) is a dynamical algebra for which the Hamiltonian is a function of the algebra generators. However, it remains uncertain if a dynamical algebra inevitably allow for an algebraic reformulation of the classical theory in terms of co-adjoint orbits.
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