Pulsating curves of zero velocity for infinitesimal mass around oblate and triaxial rigid body of triangular equilibrium points in elliptical restricted three body problem

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


    This paper explore pulsating Curves of zero velocityof the infinitesimal mass around the triangular equilibrium points with oblate and triaxial rigid body in the elliptical restricted three body problem(ER3BP).


  • Keywords


    Er3bp;Triaxiality; Dynamical System; Zero Velocity Curve; Triangular Points.

  • References


      [1] Danby JMA (1964), Stability of the triangular points in the elliptical restricted problem of three bodies, Astronomical Journal, 69,166-174.

      [2] Bennet A (1965), Characteristic exponents of the five equilibrium solutions in the EllipticallyRestricted Problem, ICARUS 4, 177-187.https://doi.org/10.1016/0019-1035(65)90060-6.

      [3] Szebehely V (1975), Stability of the points of equilibrium in restricted problem, Astronomical Journal, 72, 7-9.https://doi.org/10.1086/110195.

      [4] Szebehely V (1967), Theory of Orbits, Academic press, New-York.

      [5] Markeev A P (1978), Libration points in celestial mechanics and cosmic dynamics, NAUKA Moscow, 312.

      [6] Grebnikov E A (1964), On the stability of the Lagrangian triangle solutions of the restricted elliptic three body problem, Soviet Astronomy,8, No.3, 567-578.

      [7] Grebnikov E A (1986), the methods of Averaging Applications, NAUKA, Moscow Revised.

      [8] Gyorgyey J (1985), on the non-linear motions around the elliptical restricted problem of three bodies, Celestial Mechanics and Dynamical Astronomy, 36, No.3, 281-285.https://doi.org/10.1007/BF01230741.

      [9] KumarV &ChoudharyRK (1990), Non-linear stability of the triangular libration points for the photogravitationalelliptic restrictedproblem of three bodies, Celestial Mechanics and Dynamical Astronomy, 48, No.4, 299-317.https://doi.org/10.1007/BF00049387.

      [10] Kumar S &Ishwar B (2009), Solutions of Generalized Photogravitational Elliptical Restricted ThreeBody Problem, AIP Conf.Proc, 1146,456.https://doi.org/10.1063/1.3183564.

      [11] MarkellosV V, PerdiosE &LabrapoulouP(1992), Linear stability of the triangular equilibrium points in the photogravitationalelliptic restrictedthree body problem, Astrophysics and Space Science ,194, 207-214.https://doi.org/10.1007/BF00643991.

      [12] ZimvoschikovA S &Thkai V N (2004), Instability of libration points and resonance phenomena in the photogravitationalellipticalrestricted three bodyproblem, Solar system research, 38(2), 155-163.https://doi.org/10.1023/B:SOLS.0000022826.31475.a7.

      [13] AmmarMK (2008), The effect of solar radiation pressure on the Lagrangian points in the elliptical restricted three body problem, Astrophysics and Space Science, 313 , 393-408.https://doi.org/10.1007/s10509-007-9709-z.

      [14] Singh, J &Aishetu U (2012a), Motion in the photogravitationalellipticrestrictedthree body problem under an oblate primary, Astronomical Journal, 143, No.5, 109.https://doi.org/10.1088/0004-6256/143/5/109.

      [15] Singh J &Aishetu U (2012b), On the stability of triangular points in the ellipticrestrictedthree bodies under the radiating and oblate Primaries, Astrophysics and Space Science ,341, 349-358.https://doi.org/10.1007/s10509-012-1109-3.

      [16] Narayan a&Usha T (2014), Stability of triangular equilibrium points in the elliptic restricted problem of three bodies with radiation and triaxial primaries, Astrophysics and Space Science, 351(1), 135-142.https://doi.org/10.1007/s10509-014-1818-x.

      [17] UshaT, NarayanA&Ishwar B (2014), Effects of radiation and triaxiality of primaries on triangular equilibrium points in elliptic restricted three body problem, Astrophysics and Space Science, 349(1), 151-164.https://doi.org/10.1007/s10509-013-1655-3.

      [18] F aAbd El-Salam (2015), Stability of Triangular equilibrium points in the elliptic restricted three body problem with oblate and triaxial Primaries, AstrophysSpaceSci, 357:15.https://doi.org/10.1007/s10509-015-2308-5.

      [19] IshwarB &Elipe A (2001), Secular Solutions at Triangular Equilibrium Point in the Generalized Photogravitational Restricted ThreeBody Problem, Astrophysics and Space Science, 277, No.3, 437-446.https://doi.org/10.1023/A:1012528929233.

      [20] Subbarao PV & Sharma R K (1975), A Note on the Stability of the Triangular points of Equilibrium in the Restricted-Three body problem, Astronomy and Astrophysics, 43,381-383.

      [21] KhannaM &Bhatnagar K B (1998), Existence and Stability of the Libration points in the restricted three body problem when the smaller primary is a triaxial rigid body, Indian Journal of Pure and Applied Mathematics,29(10), 1011-1023.


 

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Article ID: 7025
 
DOI: 10.14419/ijaa.v5i1.7025




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