Area-preserving mappings and deterministic chaos for nearly parabolic motions |
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| Authors: | T Y Petrosky R Broucke |
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| Institution: | (1) Center for Studies in Statistical Mechanics, The University of Texas at Austin, 78712 Austin, Texas;(2) Department of Aerospace Engineering, The University of Texas at Austin, 78712 Austin, Texas |
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| Abstract: | The present work investigates a mechanism of capturing processes in the restricted three-body problem. The work has been done in a set of variables which is close to Delaunay's elements but which allows for the transition from elliptic to hyperbolic orbits. The small denominator difficulty in the perturbation theory is overcome by embedding the small denominator in an analytic function through a suitable analytic continuation. The results indicate that motions in nearly parabolic orbits can become chaotic even though the model is deterministic. The theoretical results are compared with numerical results, showing an agreement of about one percent. Some possible applications to cometary orbits are also given. |
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