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Nonlinear approximation of periodic three-body motions around collinear equilibrium configurations

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Analytic approximations of the second order with respect to a small orbital parameter are given for coplanar periodic motions of three finite mass points in the neighbourhood of their collinear equilibrium configurations. The expressions obtained are tested for accuracy against the ‘exact’ motions determined by numerical integration of the general three-body problem. Limiting cases of mass ratios of the three bodies are treated separately using ‘restricted’ versions of the three-body problem.

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  1. Bray, T. A. and Goudas, C. L.: 1967, in Z. Kopal (ed.),Adv. Astron. Astrophys. 5, 72.

  2. Broucke, R., Anderson, J. D., Blitzer, L., Davoust, E., and Lass, H.: 1981,Celes. Mech. 24, 63.

  3. Davoust, E. and Broucke, R.: 1982,Astron. Astrophys. 112, 305.

  4. Hénon, M.: 1969,Astron. Astrophys. 1, 223.

  5. Hénon, M.: 1973,Astron. Astrophys. 28, 415.

  6. Hénon, M.: 1974,Celes. Mech. 10, 375.

  7. Markellos, V. V.: 1981a,Celes. Mech. 25, 3.

  8. Markellos, V. V.: 1981b,Celes. Mech. 25, 319.

  9. Strömgren, E.: 1935,Publ. Copenhagen Obs., No. 100.

  10. Szebehely, V.: 1967,Theory of Orbits, Academic Press, New York.

  11. Zagouras, C. and Markellos, V. V.: 1985,Celes. Mech. 35, 257.

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Papadakis, K., Perdios, E. & Markellos, V.V. Nonlinear approximation of periodic three-body motions around collinear equilibrium configurations. Astrophys Space Sci 140, 373–383 (1988). https://doi.org/10.1007/BF00638991

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  • Mass Point
  • Analytic Approximation
  • Periodic Motion
  • Equilibrium Configuration
  • Orbital Parameter