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Abstract
In this article, we discuss the effect of earth’s oblateness and magnetic force on the motion and stability of the system for elliptic orbit of the centre of mass. We have got a set of non-linear, non-homogenous and non-autonomous equations. Generally, a system moving in space has to face some perturbative forces. These forces compel the system to change its orbit from circular to elliptic orbit. On account of this we have studied in details the problem in elliptic orbit of the centre of mass. This is simply the generalization of the particular case of the Keplerian orbit i.e. circular orbit. So, we analysed the effect of the earth’s oblateness and magnetic force on the existence and behavior of different equilibrium position of the system. Also, discuss the Jacobian Integral of the averaged equations of motion of the system, Two equilibrium solutions of the problem and after Hooke’s modulus of elasticity.
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References
Ashish Kumar & Avinash Kr Sharma (2024) “Jacobian Integral of the Equations of Motion of the system in the case of Circular Orbit of the Centre of Mass”, IJMRET Journal, Vol 9, Issue 10
Dr. Sushil Chandra Karna (2020), “Satellite: Linearized and Normalized Differential equations of Relative motion of the system”, JETIR Vol 7, Issue 6
Alimov, Yu I., “On the construction of Liapunov functions for system of linear differential equations with constant coefficient.
Chernousko, F.L. (1963) “Resonance problem in the motion of the satellite relative to its centre of mass” Journal of Computer Mathematics and Mathematical Physics, Vol. 3, PP 528-538, No. 3.
Chernousko, F.L. “About the motion of the satellite relative to its centre of mass under the action of gravitational moments” Applied Mathematics and Mechanics, Vol. 27, No. 3, PP 474-483 (Russian)
Beletsky, V.V. “About the relatice motion of two connected bodies in orbit” Kosmicheskiye Issledovania. Vol. 7, No. 3, PP 377-384, 1969 (Russian)
Beutler G. (2005). Methods of celestial mechanics. Vol. II: Application to planetary system geodynamics and satellite geodesy.Berlin: Springer. ISBN 3-540-40750-2.
A.B.J. Kuijlaars, A. Martinez-Finkelshtein and R. Orive (2005), “Orthogonality of Jacobi polynomials with general parameters. Electron, Trans, Numer, Anal., 19:1-17.
S. Zwegers,(2010) “Multivariable Appell Functions”.
Du, H, (2022) “On the Orthogonal Time and Space Relation with the Ultimate Resolution of Twin Paradox – No Differential Aging”,
DOI:10.13140/RG.2.213108.53122