Invariant rotational curves in Sitnikov's Problem

Details Invariant rotational curves in Sitnikov's Problem Invariant rotational curves in Sitnikov's Problem

Apr 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..55..351a&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 55, no. 4, p. 351-367.

Mathematics

13

Eccentric Orbits, Hamiltonian Functions, Perturbation Theory, Three Body Problem, Floquet Theorem, Kepler Laws, Matrices (Mathematics), Polar Coordinates

Scientific paper

The Sitnikov's Problem is a restricted three-body problem of celestial mechanics depending on the eccentricity, e. The Hamiltonian, H(z, v, t, e), does not depend on t if e = 0 and we have an integrable system; if e 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 of e 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 plane z = 0 as e tends to 1.

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