Numerical Study of Orbits in a non-axisymmetric potentia:

Details Numerical Study of Orbits in a non-axisymmetric potentia: Numerical Study of Orbits in a non-axisymmetric potentia:

Mar 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007aps..mard21008z&link_type=abstract

American Physical Society, APS March Meeting, March 5-9, 2007, abstract #D21.008

Physics

Scientific paper

We study the evolution of stellar objects in a given planar, non-axisymmetric gravitational potential: U(x,y),,[x^2 +(y/b)^2], with b,,. This lack of symmetry introduces a variable angular momentum that, in part, leads to a set of unusual orbits not found in conventional mechanics books. In summary, this exercise raises several interesting features: the potential is scale free, it is anisotropic, close to the origin the potential appears as a two dimensional harmonic oscillator. It has to be solved numerically (even in the case of an isotropic (b=1) logarithmic potential) to learn about the different families of orbits that contains. We provide the program that displays the different orbits. We use a spreadsheet to make the method closer to the students. It is, in our opinion, a useful research problem for an upper level undergraduate student. Finally, in place of taking two orbits and examine them exhaustively, we have preferred to give a wide spectrum of possibilities and the program to study them in more detail.

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