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arXiv · 0909.5478

Smoothed dynamics in the central field problem

Manuele Santoprete·Cristina Stoica
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Abstract

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 $α\geq 2,$ smoothing introduces fake orbits. Further, we argue that for $α\geq 2,$ smoothing should be applied to the amended potential $c/(2r^2)-1/r^α,$ where $c$ denotes the angular momentum constant.

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Manuele Santoprete, Cristina Stoica. 2009-09-30. Smoothed dynamics in the central field problem. https://doi.org/10.1016/j.nonrwa.2008.02.027

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