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

Edward Belbruno ()
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Edward Belbruno: Program of Applied and Computational Mathematics, Princeton University

A chapter in New Advances in Celestial Mechanics and Hamiltonian Systems, 2004, pp 37-61 from Springer

Abstract: 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].

Keywords: periodic orbits; Hill’s problem; continuation; zero-velocity curves (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-9058-7_3

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DOI: 10.1007/978-1-4419-9058-7_3

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