Phase space reconstruction in the restricted three-body problem

Details Phase space reconstruction in the restricted three-body problem Phase space reconstruction in the restricted three-body problem

Feb 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007aipc..886..139g&link_type=abstract

NEW TRENDS IN ASTRODYNAMICS AND APPLICATIONS III. AIP Conference Proceedings, Volume 886, pp. 139-152 (2007).

Nonlinear Sciences

Chaotic Dynamics

1

Celestial Mechanics, Celestial Mechanics, Chaotic Dynamics, Numerical Simulations Of Chaotic Systems, Time Series Analysis

Scientific paper

We study the motion of the infinitesimal mass in the planar circular restricted three-body problem. The infinitesimal mass can undergo regular or chaotic motions. It can be captured by one of the primaries, it can make transfers from one primary to another, or it can even escape those captures. We analyze through statistical methods the time-series given by the time intervals between successive crossings made by the infinitesimal particle to a given Poincaré section. We apply Takens/Yorke embedding theory to reconstruct the phase space from these time series, and we use the correlation dimension of the reconstructed phase space as a tool to distinguish between various types of motions.

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