International Journal of Mathematics Trends and Technology
Volume 9 | Number 2 | Year 2014 | Article Id. IJMTT-V9P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V9P517
We have studied the non-linear oscillation of the system of the satellites connected by light, flexible and extensible cable under the influence of 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 of the system having 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.
[1] Beletsky, V. V, About the Relative Motion of Two Connected Bodies in orbit. Kosmicheskiye Isseldovania, vol. 7, No. 6, pp. 827 - 840, 1969 (Russian).
[2] Thakur ; H.K, The motion of a system of two satellites connected by extensible cable, Ph.D. thesis, submitted to B.U. Muzaffarpur, 1975
[3] Singh, R. B, Three dimensional motion of system a two cable-connected satellite in orbit. Astronautica, acta, vol. 18, pp. 301 - 308, 1973
[4] Singh, A. K. P, Effect of Earth’s Shadow on the motion of a system of two Satellites connected by extensible cable under the influence of solar radiation pressure, Ph. D. Thesis Submitted to Bihar University, Muzaffarpur, 1990.
[5] Singh; R.B., The motion of two connected bodies in an elliptical orbit. Bulletin of the Moscow state university mathematics-mechanics. No. 3, P.P.82-86, 1973 (Russian)
[6] Kumar. V and Kumari. N, Effect of the earth’s oblateness, the shadow of the earth due to the solar radiation pressure and magnetic force on the motion and stability of two satellites
connected by an extensible cable in circular orbit of the centre of mass. IOSR-JM Volume 10, Issue 10, Oct. 2013
[7] Kumar. V and Kumari. N, Jacobian integral and Stability of the equilibrium position of the centre of mass of an extensible cable connected satellites system in the elliptic orbit motions. IJSER, Volume 4, Issue 9, September-2013
[8] A. Narayan, R.B. Singh, Non-linear non-reasonance oscillation of inter-connected satellites system under the solar pressure about the position of equilibrium for small eccentricity, Proc. Nat. Acad. Sci., India (1987), 427-437.
[9] B.M. Singh, A. Narayan, R.B. Singh, Non-linear effects in the motion and stability of an inter connected satellites system orbiting around an oblate Earth, Proc. Nat. Acad. Sci., India, 71 (2001), 225-235.
[10] S.K. Das, P.K. Bhattacharya, R.B. Singh, Effects of magnetic force on the motion of system of two cable connected satellite in orbit, Proc. Nat. Acad. Sci. India (1976), 287-299.
[11] Kumar,V. Ph.D. Thesis submitted to B.R. Ambedkar, Bihar University, Muzaffarpur,2013
Vijay Kumar, "Effect of Shadow of the Earth Due to Solar Radiation Pressure, Magnetic Force and Earth’s Oblateness on the Non-Linear Oscillation of the System in a Circular Orbit of the Centre of Mass of the Systems," International Journal of Mathematics Trends and Technology (IJMTT), vol. 9, no. 2, pp. 148-152, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V9P517
PDF 
Abstract 
Keywords 
References 
Citation