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Bifurcation diagram; Poincaré section map; Lyapunov exponents; perturbed satellite systems

In this paper,we study the qualitative behaviour of satellite systems using bifurcation diagrams, Poincaré section, Lyapunov exponents, dissipation, equilibrium points, Kaplan–Yorke dimension etc. Bifurcation diagrams with respect to the known parameters of satellite systems are analysed. Poincaré sections with different sowing axes of the satellite are drawn. Eigenvalues of Jacobian matrices for the satellite system at different equilibrium points are calculated to justify the unstable regions. Lyapunov exponents are estimated. From these studies, chaosin satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the considered system.

AYUB KHAN¹ SANJAY KUMAR¹

1. Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110 025, India

Published

10 January 2018

Manuscript received

18 April 2017

Manuscript revised

13 August 2017

Accepted

18 August 2017

Early published

Unedited version published online

Final version published online

27 December 2017