Invariant rotational curves in Sitnikov's Problem |
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| Authors: | J Martínez Alfaro Cristina Chiralt |
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| Institution: | (1) Department de Matemàtica Aplicada i Astronomia, Facultat de Matemàtiques, Universitat de València, Spain;(2) Department de Matemàtiques i Informàtica, Universitat Jaume I, Castelló, Spain |
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| Abstract: | The Sitnikov's Problem is a Restricted Three-Body Problem of Celestial Mechanics depending on a parameter, the eccentricity,e. The Hamiltonian,H(z, v, t, e), does not depend ont ife=0 and we have an integrable system; ife is small the KAM Theory proves the existence of invariant rotational curves, IRC. For larger eccentricities, we show that there exist two complementary sequences of intervals of values ofe that accumulate to the maximum admissible value of the eccentricity, 1, and such that, for one of the sequences IRC around a fixed point persist. Moreover, they shrink to the planez=0 ase tends to 1. |
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| Keywords: | Sitnikov's problem invariant rotational curves stability |
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