Physics – Classical Physics
Scientific paper
2009-08-07
Physics
Classical Physics
9 pages, 14 figures
Scientific paper
In this letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al [1] predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well.
Horwitz Larry
Levitan Jacob
Lewkowicz Meir
Yahalom Asher
No associations
LandOfFree
Lyapunov vs. Geometrical Stability Analysis of the Kepler and the Restricted Three Body 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 Lyapunov vs. Geometrical Stability Analysis of the Kepler and the Restricted Three Body Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lyapunov vs. Geometrical Stability Analysis of the Kepler and the Restricted Three Body Problem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-359770