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The problem of stability of the triangular libration points in the planarcircular restricted three-body problem is considered. A software package,intended for normalization of autonomous Hamiltonian systems by means ofcomputer algebra, is designed so that normalization problems of high analyticalcomplexity could be solved. It is used to obtain the Birkhoff normal form ofthe Hamiltonian in the given problem. The normalization is carried out up tothe 6th order of expansion of the Hamiltonian in the coordinates and momenta.Analytical expressions for the coefficients of the normal form of the 6th orderare derived. Though intermediary expressions occupy gigabytes of the computermemory, the obtained coefficients of the normal form are compact enough forpresentation in typographic format. The analogue of the Deprit formula for thestability criterion is derived in the 6th order of normalization. The obtainedfloating-point numerical values for the normal form coefficients and thestability criterion confirm the results by Markeev (1969) and Coppola and Rand(1989), while the obtained analytical and exact numeric expressions confirm theresults by Meyer and Schmidt (1986) and Schmidt (1989). The given computationalproblem is solved without constructing a specialized algebraic processor, i.e.,the designed computer algebra package has a broad field of applicability.

Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points