Friday, September 7, 2012

1209.1342 (S. R. Valluri et al.)

A Study of the Orbits of the Logarithmic Potential for Galaxies    [PDF]

S. R. Valluri, P. A. Wiegert, J. Drozd, M. DaSilva
The logarithmic potential is of great interest and relevance in the study of the dynamics of galaxies. Some small corrections to the work of Contopoulos & Seimenis (1990) who used the method of Prendergast (1982) to find periodic orbits and bifurcations within such a potential are presented. The solution of the orbital radial equation for the purely radial logarithmic potential is then considered using the p-ellipse (precessing ellipse) method pioneered by Struck (2006). This differential orbital equation is a special case of the generalized Burgers equation. The apsidal angle is also determined, both numerically as well as analytically by means of the Lambert W and the Polylogarithm functions. The use of these functions in computing the gravitational lensing produced by logarithmic potentials is discussed.
View original: http://arxiv.org/abs/1209.1342

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