A study of the orbits of the logarithmic potential for galaxies

作者：Valluri S R^*; Wiegert P A; Drozd J; Da Silva M

来源：Monthly Notices of the Royal Astronomical Society, 2012, 427(3): 2392-2400.

DOI：10.1111/j.1365-2966.2012.22071.x

• celestial mechanics
• galaxies: kinematics and dynamics

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 who used the method of Prendergast 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 precessing ellipse (p-ellipse) method pioneered by Struck. This differential orbital equation is a special case of the generalized Burgers equation. The apsidal angle is also determined, both numerically and analytically by means of the Lambert W and the polylogarithmic functions. The use of these functions in computing the gravitational lensing produced by logarithmic potentials is discussed.

• 出版日期2012-12