On the stability of the triangular libration points: exact results
نویسنده
چکیده
The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. An especially designed software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is used to obtain normal forms of the Hamiltonian in the given problem. The normalization is carried out up to the 6th order of expansion of the Hamiltonian in the coordinates and momenta. Analytical expressions for the coefficients of the normal form of the 6th order are derived. Though intermediary expressions occupy gigabytes of the computer memory, the obtained coefficients of the normal form are compact enough for presentation in typographic format. An analogue of the Deprit formula for the stability criterion is derived in the 6th order of normalization. This closes the long history of the stability analysis in the given problem completely. The attaining of this technical result has required development of intricate software as well as employing computing resources that became available only recently.
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