Astronomy and Astrophysics – Astronomy
Scientific paper
Jun 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994mnras.268.1033k&link_type=abstract
Monthly Notices of the Royal Astronomical Society, Vol. 268, p. 1033-1040 (1994)
Astronomy and Astrophysics
Astronomy
21
Celestial Mechanics, Stellar Dynamics - Galaxies: Kinematics And Dynamics
Scientific paper
The scheme introduced by McGill & Binney and Binney & Kumar (Papers I and II), for the construction of phase-space tori that are approximate invariant tori of a given Hamiltonian, is extended and refined. Whereas Papers I and II concentrated on orbits in the meridional planes of axisymmetric potentials, here tori are constructed for box and loop orbits in planar, barred potentials. We demonstrate the applicability of the scheme to potentials that have two major orbit families rather than the single family of the meridional-plane problem. We refine the methods of Papers I and II in two respects: (i) by combining the generating function approach of Paper I with point transformations, we are able to map toy tori into target tori that are not otherwise accessible; (ii) we introduce a scheme for the recovery of angle variables that is superior to that introduced in Paper II. We illustrate the method by applying it both to potentials and to potentials that are not separable and in which not all orbits belong to the two major orbit families of Stäckel potentials.
Binney James
Kaasalainen Mikko
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