An algorithm for the systematic construction of solutions to perturbed problems Original Research Article

Our task in this paper is to develop a new systematic algorithm valid to integrate a wide range of perturbed problems, or better, to calculate truncated solutions to these problems. This algorithm is related with the Newton-Puiseux construction used in the study of singularities of algebraic plane curves. We will optimize our algorithm by introducing an effective truncation technique in a similar way to that introduced by the first author to integrate some kinds of differential equations. This truncation technique will, computationally, be very important because it avoids the unnecessary calculation of very large coefficients. Strained coordinates, and initial conditions depending on the small 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 will be used to give reference solutions to an arbitrary equatorial satellite in BF variables.