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The problem of computation of the Hamiltonian for the perturbed motion of an artificial Earth satellite with large eccentricity is considered. The method of calculation of items of the perturbing function, which is presented in the form of Jacobi nome series, is described. Some advantages of the new approach to the expansion of the Hamiltonian are shown by computations within computer algebra systems. Mathematical techniques for computations with elliptic functions, which are used in the suggested method of Hamiltonian expansion, are considered. Numerical verification and accuracy checking of analytical results is investigated by means of computer algebra system MAPLE.

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