A rotating Staeckel potential

Details A rotating Staeckel potential A rotating Staeckel potential

Apr 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992apj...389..118c&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 389, April 10, 1992, p. 118-128.

Astronomy and Astrophysics

Astrophysics

9

Celestial Mechanics, Galactic Rotation, Hamiltonian Functions, Orbit Calculation, Potential Theory, Stellar Motions, Degrees Of Freedom, Density Distribution, Gravitational Fields, Mass Distribution

Scientific paper

A rotating potential, which has a second integral, besides the Hamiltonian, quadratic in the momenta, is examined. This can be expressed as a Staeckel potential in elliptic coordinates, but it is nonseparable, unless its rotation is zero. The canonical momenta are found to correspond to the elliptic coordinates and the forms of the Hamiltonian and of the new integral in elliptic coordinates and momenta. The forms of the orbits are found numerically and analytically. In the nonrotating case the orbits fill either an ellipse around both foci, or a region around one focus limited by an ellipse and a hyperbola. In the rotating case the orbits are tubes, either around both foci or around only one focus. The periodic orbits are derived analytically.

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