Finding periodic orbits with generating functions
نویسندگان
چکیده
Periodic orbits are studied using generating functions. We develop necessary and sufficient 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 orbits and around the Libration points in the three-body problem. Graduate Student Research Assistant, PhD Candidate, 734 936 0541, [email protected] Associate Professor, Senior Member AIAA, [email protected]
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