The Non-Linear Oscillation of the Centre of Mass of the System in Elliptic Orbit under the Influence of the Shadow of the Earth due to Solar Radiation Pressure, Magnetic Force and oblateness of the Earth

Vijay Kumar

doi:https://doi.org/10.14445/22315373/IJMTT-V12P516

International Journal of Mathematics Trends and Technology

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Volume 12 | Number 2 | Year 2014 | Article Id. IJMTT-V12P516 | DOI : https://doi.org/10.14445/22315373/IJMTT-V12P516

The Non-Linear Oscillation of the Centre of Mass of the System in Elliptic Orbit under the Influence of the Shadow of the Earth due to Solar Radiation Pressure, Magnetic Force and oblateness of the Earth

Vijay Kumar

Citation :

Vijay Kumar, "The Non-Linear Oscillation of the Centre of Mass of the System in Elliptic Orbit under the Influence of the Shadow of the Earth due to Solar Radiation Pressure, Magnetic Force and oblateness of the Earth," International Journal of Mathematics Trends and Technology (IJMTT), vol. 12, no. 2, pp. 102-111, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V12P516

Abstract

We have studied the non-linear oscillation of the system of the satellites connected by light, flexible and extensible cable under the influence of Earth’s magnetic force, the shadow of the earth due to solar radiation pressure and earth oblateness in the case of circular orbit of the Centre of mass of the system. The non-linear terms present in the equations of motion of the system are taken into consideration. First of all we have derived equations of motion for non-linear oscillations and a system of equation representing almost periodic oscillations due to Malkin. An attempt has been made to analyse the motion and stability of the system analytically. As there is no periodic terms in the equation of motion, so only non-resonant solution have been obtained and shown to be stable.

Keywords

Stability, Non-linear oscillation ,Solar radiation pressure, Earth magnetic force, Satellites, Elliptic orbit.

References

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