Open Access
Research Article
Analysis of Resonant Curve and Phase Portrait Due to Earth’s Equatorial Ellipticity In the Earth-Moon System Using Perturbation Technique
Sushil YadavDepartment of MathematicsMaharaja Agrasen CollegeUniversity of Delhi, Delhi, 110096, IndiaView full profile → , *Mukesh KumarCorresponding authormukesh@shivaji.du.ac.inDepartment of MathematicsShivaji CollegeUniversity of Delhi, Delhi, 110027, IndiaView full profile → , Virendra KumarDepartment of MathematicsDaulat Ram CollegeUniversity of Delhi, Delhi, 110007, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 11 Jan 2021
- Accepted:
- 17 Aug 2022
- Published Online:
- 13 Nov 2022
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- 1726037X.2022.2120272
- Pages:
- 275–298
Abstract
In this paper, the resonance due to equatorial ellipticity of Earth, spin rate of Earth and angular velocity of bary-center are investigated. Using spherical coordinate system, we have determined equations of motion of the moon. By using perturbations relative to moon, equations of motion are simplified to second order ordinary differential equation containing the equatorial ellipticity parameter of the Earth. Two types of resonant curves due to the frequencies (a) , and (b) are analyzed. It is observed that the amplitudes of the oscillation are different at different resonant points due to different size of the bandwidth. Finally, the phase portrait of the orbits of the moon and the phase spaces are analyzed by using Poincare section with periodicity in time t for the unpertubed system.
Keywords
Subject Classifications
54H20
References
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