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Librations of central configurations and braided Saturn rings

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Abstract

We give a simple mathematical model for braided rings of a planet based on Maxwell's model for the rings of Saturn.

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References

  • Davies, I., Truman, A. and Williams, D.: 1983, Classical periodic solutions of the equal-mass 2n-body problem, 2n-ion problem and then-electron atom problem,Phys. Lett. 99A, 15.

    Google Scholar 

  • Davies, I., Truman, A. and Williams, D. (in prep.): Classical periodic orbits for equal-mass many body systems, preprint.

  • Deprit, A.: 1969, Canonical transformations depending on a small parameter,Celest. Mech. 1, 12–30.

    Google Scholar 

  • Guillemin, V. and Sternberg, A.: 1984,Symplectic Techniques in Physics, Cambridge Univ. Press, Cambridge.

    Google Scholar 

  • Lissauer, J. and Peale, S.: 1986, The production of ‘braids’ in Saturn'sF Ring,Icarus 67, 358–374.

    Google Scholar 

  • Marsden, J. and Weinstein, A.: 1974, Reduction on symplectic manifolds with symmetries,Rep. Math. Phys. 5, 121–130.

    Google Scholar 

  • Maxwell, J.C.: 1859,On the Stability of the Motion of Saturn's Rings, Maxmillan & Co., London.

    Google Scholar 

  • Meyer, K.: 1973, Symmetries and integrals in mechanics, in M. Peixoto (ed.),Dynamical Systems Academic Press, New York, pp. 259–273.

    Google Scholar 

  • Meyer, K.: 1981, Hamiltonian systems with a discrete symmetry,J. Diff. Eq. 41, 228–238.

    Google Scholar 

  • Meyer, K. and Hall, G.: 1991,Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Springer-Verlag, New York.

    Google Scholar 

  • Moeckel, R.: 1992, Linear stability of relative equilibra with a dominate mass, preprint.

  • Smith, B.et al.: 1981, Encounter with Saturn: Voyager 1 image science results,Science 212, 163–190.

    Google Scholar 

  • Smith, B.et al.: 1982, A new look at the Saturn system: Voyager 2 images,Science 215, 504–536.

    Google Scholar 

  • Weinstein, A.: 1973, Normal modes for non-linear Hamiltonian systems,Inv. Math. 20, 47–57.

    Google Scholar 

  • Wintner, A.: 1944,The Analytic Foundations of Celestial Mechanics, Princeton University Press, Princeton, NJ.

    Google Scholar 

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Meyer, K.R., Schmidt, D.S. Librations of central configurations and braided Saturn rings. Celestial Mech Dyn Astr 55, 289–303 (1993). https://doi.org/10.1007/BF00692516

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  • DOI: https://doi.org/10.1007/BF00692516

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