Statistics – Computation
Scientific paper
Sep 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990cemda..49..233e&link_type=abstract
Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 49, no. 3, 1990, p. 233-247.
Statistics
Computation
Celestial Mechanics, Computational Astrophysics, Equations Of Motion, Galaxies, Orbit Perturbation, Centrifugal Force, Cylindrical Coordinates, Degrees Of Freedom, Hamiltonian Functions
Scientific paper
The equations of motion for stars in the Galaxy are investigated analytically and numerically. Each star is modeled as a point in six-dimensional phase space, so that the solution of the equations involves finding six independent integrals: each equation represents a hypersurface in phase space, and the trajectory is the intersection of the six hypersurfaces. The potential energy is assumed to be independent of time, and the case where the potential has axial symmetry about a fixed direction in space is considered. Separation of variables is applied to generate phase portraits at different points; complete solutions are obtained using Weierstrass elliptic functions; and periodic orbits are determined numerically by the fixed-point method of Poincare (1957) and presented graphically.
El-Sabaa M. F. F.
Sherief H. H.
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