Smoothed dynamics in the central field problem

Details Smoothed dynamics in the central field problem Smoothed dynamics in the central field problem

2009-09-30

arxiv.org/abs/0909.5478v1

Nonlinear Analysis: Real World Applications Volume 10, Issue 3, June 2009, Pages 1870-1881

Physics

Mathematical Physics

17 pages, 8 figures

Scientific paper

10.1016/j.nonrwa.2008.02.027

Consider the motion of a material point of unit mass in a central field determined by a homogeneous potential of the form $(-1/r^{\alpha})$, $\alpha>0,$ 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 $\alpha < 2,$ while for $\alpha \geq 2,$ smoothing introduces fake orbits. Further, we argue that for $\alpha\geq 2,$ smoothing should be applied to the amended potential $c/(2r^2)-1/r^{\alpha},$ where $c$ denotes the angular momentum constant.

Affiliated with

Also associated with

No associations

Rating

Smoothed dynamics in the central field problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Smoothed dynamics in the central field problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Smoothed dynamics in the central field problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-588672