Smoothed dynamics in the central field problem

✍ Scribed by Manuele Santoprete; Cristina Stoica

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 801 KB
• Volume: 10
• Category: Article
• ISSN: 1468-1218
• DOI: 10.1016/j.nonrwa.2008.02.027

✦ Synopsis

Consider the motion of a material point of unit mass in a central field determined by a homogeneous potential of the form (-1/r α ), α > 0, where r being the distance to the centre of the field. Due to the singularity at r = 0, in computer-based simulations, usually, the potential is replaced by a similar potential that is smooth, or at least continuous.

In this paper, we compare the global flows given by the smoothed and non-smoothed potentials. It is shown that the two flows are topologically equivalent for α < 2, while for α ≥ 2, smoothing introduces fake orbits. Further, we argue that for α ≥ 2, smoothing should be applied to the amended potential c/(2r 2 ) -1/r α , where c denotes the angular momentum constant.