Symbolic Computation of the Averaged Hamiltonian Describing the Motion of Asteroids under the Influence of Major Planets

A semianalytic theory of motion of minor planets is constructed by means of the Lie-series method involving the Le Verrier expansions of the planetary disturbing function. The averaging procedure is realized symbolically by means of the computer algebra system MAPLE. The averaged Hamiltonian is used for symbolic computation of the right-hand parts of the canonical differential equations of motion. The equations are integrated numerically by means of traditional numerical software. Bibliography: 9 titles.