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Abstract: Periodic orbits are studied using generating functions. We develop necessary and su#cient conditions for existence of periodic orbits of a given period or going through a given point in space. These conditions reduce the search to either solving a set of implicit equations, which can often be done graphically, or finding the roots of an equation of one variable only, independent of the Hamiltonian system considered. We apply our results to periodic orbits in the vicinity of other periodic... (Update)
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BibTeX entry: (Update)
@misc{ scheeres-finding,
author = "Functions Guibout Scheeres",
title = "Finding Periodic Orbits With Generating",
url = "citeseer.ist.psu.edu/685729.html" }
Citations (may not include all citations):235 Classical Mechanics (context) - Goldstein - 1965
114 Generalized solutions of Hamilton-Jacobi equations (context) - Lions - 1982
11 Les Methodes Nouvelles de la Mecanique Celeste (context) - Poincare - 1957
8 Some aspects of the dynamics and numerics of hamiltonian sys.. (context) - MacKay - 1990
2 An iterative algorithm for solving hamilton-jacobi type equa.. (context) - Markman, Katz - 2000
1 Generating families in the restricted three-body problem (context) - Henon - 1997
1 Formation flight with generating functions: Solving the rela.. (context) - Guibout, Scheeres - 2002
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