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Construction of Periodic Orbits in Hill’s Problem for $$C \gtrsim {3^{\tfrac{4}{3}}}$$

In: New Advances in Celestial Mechanics and Hamiltonian Systems

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  • Edward Belbruno

    (Program of Applied and Computational Mathematics, Princeton University)

Abstract

Periodic orbits of the classical Hill families g, g for $$C \gtrsim {3^{\tfrac{4}{3}}}$$ are numerically constructed as a homotopic continuation of a special family of periodic orbits of a truncated system of differential equations of Hill’s problem. A subset of periodic orbits along the continuation are shown to move arbitrarily near to the zero velocity curves for all time. The differential equations of Hill’s problem are transformed to coordinates relative to the zero-velocity curves. This paper summarizes the results of [1].

Suggested Citation

  • Edward Belbruno, 2004. "Construction of Periodic Orbits in Hill’s Problem for $$C \gtrsim {3^{\tfrac{4}{3}}}$$," Springer Books, in: J. Delgado & E. A. Lacomba & J. Llibre & E. Pérez-Chavela (ed.), New Advances in Celestial Mechanics and Hamiltonian Systems, pages 37-61, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-9058-7_3
    DOI: 10.1007/978-1-4419-9058-7_3
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