A1 Refereed original research article in a scientific journal
L-3 DYNAMICS AND POINCARE MAPS IN THE RESTRICTED FULL THREE BODY PROBLEM
Authors: Pihajoki P, Herrera-Sucarrat E, Palmer P, Roberts M
Publisher: INST THEORETICAL PHYSICS ASTRONOMY
Publication year: 2012
Journal: Baltic Astronomy
Journal name in source: BALTIC ASTRONOMY
Journal acronym: BALT ASTRON
Number in series: 3
Volume: 21
Issue: 3
First page : 271
Last page: 297
Number of pages: 27
ISSN: 1392-0049
Web address : http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012BaltA..21..271P&link_type=ARTICLE&db_key=AST&high=
Abstract
Poincare maps are a basic dynamical systems tool yielding information about the geometric structure of the phase space of the system. Poincare maps are however time consuming to compute. In this paper we have analysed and compared two different schemes to compute Poincare maps in the context of accuracy versus computation time: a Runge-Kutta method of 7th and 8th order and a time transformed geometric method of 6th order. The dynamical system used is the Restricted Full Three Body Problem, with the primaries, an elongated body and a sphere, in a short axis relative equilibrium configuration. Using these Poincare maps we have studied the dynamics near the collinear Lagrange point L-3, located on the outer side of the elongated body. We present evidence that the L-3 point in this system can have saddle-center, stable or complex unstable behaviour depending on system parameters. We further show that when a low accuracy regime that still captures the correct structure of the Poincare map is considered, the geometric method clearly out-performs the Runge-Kutta method being up to 4 times faster to compute and free from accumulating local errors that smear the structure of the Poincare maps.
Poincare maps are a basic dynamical systems tool yielding information about the geometric structure of the phase space of the system. Poincare maps are however time consuming to compute. In this paper we have analysed and compared two different schemes to compute Poincare maps in the context of accuracy versus computation time: a Runge-Kutta method of 7th and 8th order and a time transformed geometric method of 6th order. The dynamical system used is the Restricted Full Three Body Problem, with the primaries, an elongated body and a sphere, in a short axis relative equilibrium configuration. Using these Poincare maps we have studied the dynamics near the collinear Lagrange point L-3, located on the outer side of the elongated body. We present evidence that the L-3 point in this system can have saddle-center, stable or complex unstable behaviour depending on system parameters. We further show that when a low accuracy regime that still captures the correct structure of the Poincare map is considered, the geometric method clearly out-performs the Runge-Kutta method being up to 4 times faster to compute and free from accumulating local errors that smear the structure of the Poincare maps.
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