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Generalized Hill's problem: Some cases of complete integrability

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Abstract

In this paper, we are investigating cases of integrability in the planar Hill's problem. The external potential U extis supposed to be time independent in a given uniformly rotating frame. Cases of integrability of the relative motion of two interacting particles in the vicinity of an equilibrium solution of U extare found. In all these cases, the form of the second integral is explicitly given, the first being the Jacobian one. Cases in which the interacting potential U between the two particles is of newtonian type are particularized.

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References

  • Bozis, G.: 1982, ‘Compatibility Conditions for a Non-quadratic Integral of Motion’, Celest. Mech. 28, 367–380

    Google Scholar 

  • Chauvineau, B.: 1991, ‘Generalized Hill's Problem. Case of an External Field of Force Deriving from a Central Potential‘, Celest. Mech. 51, 119–129

    Google Scholar 

  • Chauvineau, B. and Mignard, F.: 1990, ‘Generalized Hill's Problem: Lagrangian Hill's Case’, Celest. Mech. 47, 123–144

    Google Scholar 

  • Claes, H., Henrard, J., Zune, J. M., Moons, M., and Lemaitre, A.: 1988, Guide d'utilisation du Manipulateur de Series [MS]. Internal publication. Department of Mathematics, FUNDP, Namur

    Google Scholar 

  • Dorizzi, B., Grammaticos, B., and Ramani, A.: 1983, ‘A New Class of Integrable Systems’, J. Math. Phys. 24, (9), 2282–2288, September 1983

    Google Scholar 

  • Hill, G. W.: 1877, ‘Researches in the Lunar Theory’, Amer. Jal Math. 1, 5–26, 129–147, 245–260

    Google Scholar 

  • Laskar, J.: 1990a, Description des routines utilisateur de TRIP 0.3. Bureau des Longitudes.

  • Laskar, J.: 1990b, Manipulation des series. In “Modern Methods in Celest. Mech.”. Ecole d'été Goutelas 1989. D. Benest and Cl. Froeschlé eds. Ed. Frontières.

  • Mignard, F. and Hénon, M.: 1984, ‘About an Unsuspected Integrable Problem’, Celest. Mech. 33, 239–250

    Google Scholar 

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  1. Observaloire de la Côte d'Azur Avenue Copernic, 06130, Grasse, France

    B. Chauvineau

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  1. B. Chauvineau
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Chauvineau, B. Generalized Hill's problem: Some cases of complete integrability. Celestial Mech Dyn Astr 51, 363–377 (1991). https://doi.org/10.1007/BF00052928

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  • DOI: https://doi.org/10.1007/BF00052928

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