Integrals of Motion in Kuzmin-Like Galaxy Potentials

Details Integrals of Motion in Kuzmin-Like Galaxy Potentials Integrals of Motion in Kuzmin-Like Galaxy Potentials

Nov 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001dda....32.0203t&link_type=abstract

American Astronomical Society, DDA Meeting #32, #02.03; Bulletin of the American Astronomical Society, Vol. 33, p.1188

Astronomy and Astrophysics

Astronomy

Scientific paper

We have identified an orthogonal curvilinear coordinate system (ξ 1, ξ 2, ξ 3) for which surfaces of constant ξ 1 exactly coincide with equipotential surfaces in the Kuzmin galaxy potential. The three principal coordinates are: ξ 1 ≡ [x2 + y2 + (a + |z|)2 ]1/2, ξ 2 ≡ arctan [ (|z|/z) (x2 + y2)1/2 / (a + |z|)], ξ 3 ≡ arctan [ (y/x) ]. When the equation of motion is written in terms of this ``Kuzmin'' coordinate system, the integrals of motion for particles moving in Kuzmin-like potentials are easily recognized. Specifically, any time-independent potential Φ that is a function only of ξ 1 will exhibit the same number of integrals of motion as does a spherically symmetric potential. In such Kuzmin-like potentials, the vector J ≡ e1 ξ 1 x v is the analog of the specific angular momentum vector in spherically symmetric potentials. Furthermore, in potentials of the form Φ 1/ξ 1, all three Cartesian components of the vector L ≡ [v x J + e1 (ξ 1 Φ )] --- an analog of the Laplace-Runge-Lenz vector --- also prove to be integrals of the motion. For two specific potentials --- the Kuzmin potential and a logarithmic Kuzmin-like potential --- we have derived analytical expressions defining the surfaces of section for particles in polar orbits, and in both cases have identified the domain of occupancy of box orbits, loop orbits, and periodic orbits. This work has been supported in part by the U.S. National Science Foundation through grant AST-9987344.

Affiliated with

Also associated with

No associations

Rating

Integrals of Motion in Kuzmin-Like Galaxy Potentials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Integrals of Motion in Kuzmin-Like Galaxy Potentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integrals of Motion in Kuzmin-Like Galaxy Potentials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1235575