Improved grid search method: an efficient tool for global computation of periodic orbits |
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Authors: | G A Tsirogiannis E A Perdios V V Markellos |
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Institution: | (1) Department of Engineering Sciences, University of Patras, Patras, Greece |
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Abstract: | We present an improved grid search method for the global computation of periodic orbits in model problems of Dynamics, and
the classification of these orbits into families. The method concerns symmetric periodic orbits in problems of two degrees
of freedom with a conserved quantity, and is applied here to problems of Celestial Mechanics. It consists of two main phases;
a global sampling technique in a two-dimensional space of initial conditions and a data processing procedure for the classification
(clustering) of the periodic orbits into families characterized by continuous evolution of the orbital parameters of member
orbits. The method is tested by using it to recompute known results. It is then applied with advantage to the determination
of the branch families of the family f of retrograde satellites in Hill’s Lunar problem, and to the determination of irregular families of periodic orbits in a
perturbed Hill problem, a species of families which are difficult to find by continuation methods.
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Keywords: | Families of periodic orbits Grid search Hill’ s problem Irregular families |
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