Symbolic computation of the averaged Hamiltonian, describing the motion of asteroids under the influence of major planets

The problem of developing a semianalytical theory of motion of minor planets is considered.The theory is constructed by means of Lie-series method using the Le Verrier expansions of planetary disturbing function. The averaging procedure is realized symbolically by means of computer algebra system MAPLE. The averaged Hamiltonian is used for symbolic computation of right parts of canonical differential equations of motion. These equations are integrated numerically by means of traditional numerical software.