Effect of oblateness on the non-linear stability of L 4 in the restricted three-body problem

Details Effect of oblateness on the non-linear stability of L 4 in the restricted three-body problem Effect of oblateness on the non-linear stability of L 4 in the restricted three-body problem

Sep 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cemda..65..291s&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 65, Issue 3, pp.291-312

Astronomy and Astrophysics

Astronomy

Scientific paper

Non-linear stability of the libration point L 4 of the restricted three-body problem is studied when the more massive primary is an oblate spheroid with its equatorial plane coincident with the plane of motion, Moser's conditions are utilised in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff's normal form with the help of double D'Alembert's series. It is found that L 4 is stable for all mass ratios in the range of linear stability except for the three mass ratios: begin{gathered} μ _{c1} = 0.0242{text{ }}...{text{ }}{}^{{text{__}}}0.1790{text{ }}...{text{ }}A_1 , \ μ _{c2} = 0.0135{text{ }}...{text{ }}{}^{{text{__}}}0.0993{text{ }}...{text{ }}A_1 , \ μ _{c3} = 0.0109{text{ }}...{text{ }}{}^{{text{__}}}0.0294{text{ }}...{text{ }}A_1 . \

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