On the dynamics of planar oscillations for a dumbbell satellite in J2 problem (original) (raw)

Dynamics of a dumbbell satellite under the zonal harmonic effect of an oblate body

Communications in Nonlinear Science and Numerical Simulation, 2015

The aim of the present paper is to study the dynamics of a dumbbell satellite moving in a gravity field generated by an oblate body considering the effect of the zonal harmonic parameter. We prove that the pass trajectory of the mass center of the system is periodic and different from the classical one when the effect of the zonal harmonic parameter is non zero. Moreover, we complete the classical theory showing that the equations of motion in the satellite approximation can be reduced to Beletsky's equation when the zonal harmonic parameter is zero. The main tool for proving these results is the Lindstedt-Poincare's technique.

Chaotic motion in problem of dumbell satellite

Int. J. Contemp. Math. Sciences, 2011

In our present problem we have analytically determined the chaotic parameter in the problem of a dumbell satellite. Computational studies reveal that the chaotic parameter is effective in making the regular behavior of the system chaotic.

Regular and chaotic motion of high altitude satellites

Advances in Space Research, 2007

We have computed the integrated autocorrelation function for different families of geosynchronous, inclined orbits in order to detect the regions of chaotic motion. In order to reduce the problems due to high eccentricity orbits, the logarithmic Hamiltonian regularization was applied and a symplectic integrator of the Wisdom-Holman type was implemented. The orbits were integrated for an interval of 10 000 days. The results indicate that non-predictable orbits can be found in this relatively short time in the separatrix zone of the 1 : 1 tesseral resonance. Their chaotic nature results from the interchange between libration and circulation type of motion, and from the significant eccentricity growth, caused by the Kozai-Lidov resonance. Some of these orbits intersects the Earth's surface in time shorter than 20 years for a particular initial geometry of interacting bodies.

Chaotic Oscillation of Satellite due to Aerodynamic Torque

Advances in Astronomy, 2021

This study presents the chaotic oscillation of the satellite around the Earth due to aerodynamic torque. The orbital plane of the satellite concurs is same as the tropical plane of Earth. The half-width of riotous separatrix is assessed utilizing Chirikov’s measure. Variety of boundary techniques shows that streamlined force boundary (ɛ), unpredictability of circle (e), and mass-proportion (ω0) convert normal wavering to the disorganized one. We studied the behavior of trajectories due to change in parameters with Lyapunov exponents and time series plots. The theory is applied to Resourcesat-1, an artificial satellite of the Earth.

Some Non-linear Parametric Resonance Oscillations Of Dumbell Satellite In Elliptical Orbit

International Journal of Applied Mathematical Research, 2013

Some non-linear parametric resonance oscillations of Dumbell satellite in elliptical orbit in the central gravitational field of the Earth under the combined influence of Earth magnetic field ,oblateness of the Earth and some external periodic forces of general in nature has been studied.The system comprises of two charged material particles connected by a light flexible and inextensible cable ,moves with taut cable like a dumbell satellite around the Earth in elliptical orbit.The central gravitational field of the Earth is the main force governing the motion of the system and various perturbing forces influencing the system are disturbing in nature. Non-linear oscillations of dumbbell satellite about the equilibrium position in the neighbourhood of the parametric resonance 1 2   , has been investigated, exploiting the well known asymptotic method due to Bogoliubov,Krilov and Metropoloskey , considering 'e' to be a small parameter .The analysis of stability of the system has been discussed due to Poincare method.

Bifurcation and Chaos in an Apparent-Type Gyrostat Satellite

Nonlinear Dynamics, 2005

Attitude dynamics of an asymmetrical apparent gyrostat satellite has been considered. Hamiltonian approach and Routhian are used to prove that the dynamics of the system consists of two separate parts, an integrable and a non-integrable. The integrable part shows torque free motion of gyrostat, while the non-integrable part shows the effect of rotation about the earth and asphericity of the satellite's inertia ellipsoid. Using these results, theoretically when the non-integrable part is eliminated, we are able to design a satellite with exactly regular motion. But from the engineering point of view the remaining errors of manufacturing process of the mechanical parts cause that the non-integrable part can not be eliminated, completely. So this case can not be achieved practically. Using Serret-Andoyer canonical variable the Hamiltonian transformed to a more appropriate form. In this new form the effect of the gravity, asphericity, rotational motion and spin of the rotor are explicitly distinguished. The results lead us to another way of control of chaos. To suppress the chaotic zones in the phase space, higher rotational kinetic energy can be used. Increasing the parameter related to the spin of the rotor causes the system's phase space to pass through a heteroclinic bifurcation process and for the sufficiently large magnitude of the parameter the heteroclinic structure can be eliminated. Local bifurcation of the phase space of the integrable part and global heteroclinic bifurcation of whole system's phase space are presented. The results are examined by the second order Poincaré surface of section method as a qualitative, and the Lyapunov characteristic exponents as a quantitative criterion.

The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2 : 1 Resonance

Mathematical Problems in Engineering, 2012

The orbital dynamics of synchronous satellites is studied. The 2 : 1 resonance is considered; in other words, the satellite completes two revolutions while the Earth completes one. In the development of the geopotential, the zonal harmonicsJ20andJ40and the tesseral harmonicsJ22andJ42are considered. The order of the dynamical system is reduced through successive Mathieu transformations, and the final system is solved by numerical integration. The Lyapunov exponents are used as tool to analyze the chaotic orbits.