Abstract
A Riemann ellipsoid is a classical fluid with an ellipsoidal boundary whose motion depends linearly on position. The Riemann ellipsoid Newtonian equations of motion are proven to form a Hamiltonian dynamical system. The co-adjoint orbits of a Lie group GCM(3) on which the inertia tensor is positive-definite are the reduced phase spaces of Riemann ellipsoids for which conservation of circulation has been exploited fully.
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References
Chandrasekhar, S., Ellipsoidal Figures of Equilibrium, Yale Univ., New Haven, 1969.
Lebovitz, N. R., Ap. J. 175, 171 (1972).
Carter, B. and Luminet, J. P., Monthly Notices Roy. Astron. Soc. 212, 23 (1985).
Rosenkilde, Carl E., J. Math. Phys. 8, 98 (1967).
Cohen, S., Plasil, F., and Swiatecki, W. J., Ann. Phys. (N.Y.) 82, 557 (1974).
Cusson, R. Y., Nucl. Phys. A114, 289 (1968).
Dyson, F. J., J. Math. Mech. 18, 91 (1968).
Anisimov, S. I. and Lysikov, Yu. I., Prikl. Mat. Mekh. (J. Appl. Math. Mech.) 34, 926 (1970).
Rosensteel, G. and Rowe, D. J., Ann. Phys. (N.Y.) 96, 1 (1976).
Weaver, O. L., Cusson, R. Y., and Biedenharn, L. C., Ann. Phys. (N.Y.) 102, 493 (1976).
Rosenkilde, Carl E., J. Math. Phys. 8, 88 (1967).
Gulshani, P. and Rowe, D. J., Can. J. Phys. 54, 970 (1976).
Rosensteel, G. and Ihrig, E., Ann. Phys. (N.Y.) 121, 113 (1979).
Guillemin, V. and Sternberg, S., Ann. Phys. (N.Y.) 127, 220 (1980).
Marsden, J. E., Ratiu, T., and Weinstein, A., Trans. Amer. Math. Soc. 281, 147 (1984).
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Rosensteel, G. Hamiltonian formulation of Riemann ellipsoid dynamics. Lett Math Phys 17, 79–86 (1989). https://doi.org/10.1007/BF00402322
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DOI: https://doi.org/10.1007/BF00402322