AN ALGORITHM FOR THE SYSTEMATIC CONSTRUCTION OF SOLUTIONS TO PERTURBED PROBLEMS

Our task in this paper is to develop a new systematic algorithm valid to integrate a wide range of perturbed problems, or better, to calcula te truncated solutions to these problems. This algorithm is related wi th the Newton-Puiseux construction used in the study of singularities of algebraic plane curves. We will optimize our algorithm by introduci ng an effective truncation technique in a similar way to that introduc ed by the first author to integrate some kinds of differential equatio ns. This truncation technique will, computationally, be very important because it avoids the unnecessary calculation of very large coefficie nts. Strained coordinates, and initial conditions depending on the sma ll perturbation parameter, can easily be incorporated to our algorithm and some examples will be presented. Since satellite problems can be reduced to the integration of perturbed oscillators, our techniques wi ll be used to give reference solutions to an arbitrary equatorial sate llite in BF variables. (C) 1998 Elsevier Science B.V.