Characterization of the Phase Space Structure of Circular Restricted Three-Body Problem: An Alternative Approach

Author:

Gupta Beena R.1,Kumar Vinay2

Affiliation:

1. Department of Mathematics, Lakshmibai College, University of Delhi, Delhi, India

2. Department of Mathematics, Zakir Husain Delhi College, University of Delhi, Delhi, India

Abstract

In this paper, we have considered Time-Frequency Analysis (TFA) and Poincaré Surface of Section (PSS) for the study of the phase space structure of nonlinear dynamical system. We have examined a sample of orbits taken in the framework of Circular Restricted Three-Body Problem (CRTBP). We have computed ridge-plots (i.e. time-frequency landscape) using the phase of the continuous wavelet transform. Clear visualization of resonance trappings and the transitions is an important feature of this method, which is presented using ridge-plots. The identification between periodic and quasi-periodic, chaotic sticky and nonsticky and regular and chaotic orbits are done in comparatively less time and with less computational effort. The spatial case of Circular Restricted Three-Body problem is considered to show the strength of Time-Frequency Analysis to higher dimensional systems. Also, with the help of ridge-plots, we can visualize the phenomenon of transient chaos.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

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