Melnikov-based analysis for chaotic dynamics of spin-orbit motion of a gyrostat satellite

Abstract

Interactions of the orbital motion on attitude dynamics of the gyrostat satellite are considered in this paper. The mathematical model is derived using the Hamiltonian method for the spin-orbit motion of the spacecraft followed by the reduction of the coupled equations of motion using the extended Deprit canonical transformation. The analytical Melnikov method is used innovatively to study chaos on the complex Spin-Orbit dynamics of the gyrostat satellite. Also, the numerical methods such as Lyapunov exponent criterion, Poincaré section, trajectories of phase portrait, and the time–history responses can be proved the heteroclinic bifurcation and chaotic vibrations in the highly nonlinear system. Using the results based on the Melnikov integral, the parameters of the spacecraft including the mass and inertia moment of satellite with respect to the altitude of orbit can be designed in order to control the bifurcation with a view to prevention of chaos in the system in the absence of an active control system.

Keywords

Gyrostat satellite coupled spin-orbit motion Melnikov method Lyapunov exponent chaos

Get full access to this article

View all access options for this article.

References

Inarrea

. Chaos and its control in the pitch motion of an asymmetric magnetic spacecraft in polar elliptic orbit. Chaos Solitons Fract 2009; 40: 1637–1652.

Zhou

Chen

. Stability and chaos of a damped satellite partially filled with liquid. Acta Astronaut 2009; 65: 1628–1638.

Baozeng

. Heteroclinic bifurcations in completely liquid-filled spacecraft with flexible appendage. Nonlinear Dyn 2008; 51: 317–327.

Kuang

Meehan

Leung

AYT

, et al. Nonlinear dynamics of a satellite with deployable solar panel arrays. Int J Non-Linear Mech 2004; 39: 1161–1179.

Chegini

Sadati

Salarieh

. Chaos analysis in attitude dynamics of a flexible satellite. Nonlinear Dyn 2018; 93: 1421–1438.

Wiggins S. Introduction to applied nonlinear dynamical systems and chaos. New York: Springer-Verlag, 2003.

Abtahi

Sadati

. Chaos control in attitude dynamics of a gyrostat satellite based on linearised Poincaré map estimation by support vector machine. Proc IMechE, Part K: J Multi-body Dynamics 2013; 227: 302–312.

Shirazi

Ghaffari-Saadat

. Bifurcation and chaos in an apparent-type gyrostat satellite. Nonlinear Dyn 2005; 39: 259–274.

Kuang

Meehan

Leung

AYT

. On the chaotic rotation of a liquid-filled gyrostat via the Melnikov–Holmes–Marsden integral. Int J Non-Linear Mech 2006; 41: 475–490.

10.

Elipe

Lanchares

. Exact solution of a triaxial gyrostat with one rotor. Celest Mech Dyn Astron 2008; 101: 49–68.

11.

Doroshin

. Analysis of attitude motion evolutions of variable mass gyrostats and coaxial rigid bodies system. Int J Non-Linear Mech 2010; 45: 193–205.

12.

Mahdi

. Chaotic study and chaos control in a half-vehicle model with semi-active suspension using discrete optimal Ott–Grebogi–Yorke method. Proc IMechE, Part K: J Multi-body Dynamics 2017; 231(1): 148–155. .

13.

Guzzetti

Howell

. Attitude dynamics in the circular restricted three-body problem. Astrodynamics 2018; 2: 87–119.

14.

Chegini

Sadati

. analysis in attitude dynamics of a satellite with two flexible panels. Int J Non-Linear Mech 2018; 103: 55–67.

15.

Abtahi

Sadati

Salarieh

. Nonlinear analysis and attitude control of a gyrostat satellite with chaotic dynamics using discrete-time LQR-OGY. Asian J Control 2016; 18: 1845–1855.

16.

Gurfil

Elipe

Tangren

, et al. The Serret-Andoyer formalism in rigid-body dynamics: I. Symmetries and perturbations. Regular Chaotic Dyn 2007; 12: 389–425.

17.

Abtahi

Sadati

. Ricci based chaos analysis for roto-translatory motion of a Kelvin-type gyrostat satellite. Proc IMechE, Part K: J Multi-body Dynamics 2014; 228: 34–46.

18.

Sidi MJ. Spacecraft dynamics and control: a practical engineering approach. London: Cambridge University Press, 1997.

19.

Meirovitch L. Methods of analytical dynamics. New York: McGraw-Hill, 1970.

20.

Spiegel M, Lipschutz S and Liu J. Mathematical handbook of formulas and tables. New York: McGraw-Hill Professional, 1998.