In the present paper, we have determined the equations of motion of moon in spherical coordinate system using the procedure of Frick and Garber (1962). Using perturbation equations of motion are reduced to a second order differential equation. From the solution, two types of resonance are observed, (i) due to the frequencies–rate of change of earth’s equatorial ellipticity parameter and earth’s rotation rate and (ii) due to the frequencies–angular velocity of the bary-center around the sun) and earth’s rotation rate. Resonant curves are drawn where oscillatory amplitude becomes infinitely large at the resonant points. Effect of earth’s equatorial ellipticity parameter and resistive force on the resonant curves is analyzed. From the graphs it is observed that the effect of earth’s equatorial ellipticity on the resonant curves is very small while the effect of resistive force is significant. It is also observed that oscillatory amplitude decreases when the magnitude of resistive force increases. Finally, the phase portrait is analyzed when the system is free from forces. Orbits in the phase space are also studied by applying the method of Poincare section. A necessary condition for the bifurcation is derived at the end.
Yadav, Sushil; Kumar, Mukesh; and Aggarwal, Rajiv
(R1889) Effect of Resistive Force and Earth’s Equatorial Ellipticity on Resonant Curve in the Earth-Moon System Around the Sun Using Perturbation Technique and Poincare Section,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 17,
1, Article 13.
Available at: https://digitalcommons.pvamu.edu/aam/vol17/iss1/13