Hamiltonian dynamics of self-gravitating ellipsoids

Details Hamiltonian dynamics of self-gravitating ellipsoids Hamiltonian dynamics of self-gravitating ellipsoids

Jan 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991apj...366...30r&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 366, Jan. 1, 1991, p. 30-37.

Statistics

Computation

10

Computational Astrophysics, Dynamical Systems, Ellipsoids, Galactic Structure, Gravitational Effects, Equations Of Motion, Galactic Evolution, Hamiltonian Functions, Runge-Kutta Method

Scientific paper

The virial equations of motion of the classical theory of rotating Riemann ellipsoids are demonstrated to form a Hamiltonian dynamical system. The phase space is reduced fully with respect to the conserved Kelvin circulation. The constructive method of proof is algebraic and based upon the general collective motion group GCM(3). A useful and highly accurate rational approximation is reported for the self-gravitating potential energy. Using this appoximation, the equations of motion for the principal axes oscillations of an incompressible self-gravitating fluid are defined by a polynomial vector field, and an analytic formula is given for the angular momentum and circulation of an equilibrium triaxial ellipsoid.

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