Machine derivation of the tesseral perturbation of artificial satellites

A non-conservative Lie transformation is used to establish the theory of tesseral perturbation including the cross terms from the zonal harmonic J₂ with the tesseral harmonics. The formulae for the perturbations are derived with a computer. The storage of the Poisson series is effected through a one-to-one correspondence between the multi-dimensional index of a term in the series and the store address of the coefficient of that term. Rules for storing some typical series in celestial mechanics in computers are also given.