On numerical continuation of families of periodic orbits in a parametric potential (Q1352683)

The author studies the problem of continuing numerically families of periodic orbits in a conservative dynamical systems with two degrees of freedom with respect to one of the parameters of a multiparametric potential. Following the methods and results of \textit{A. Deprit} and \textit{J. Henrard} [Astron. J. 72, 158-172 (1967; per bibl.)] who split the tangent displacement along the orbit from the normal one in variational equations the author obtains a tangent predictor valid for any kind of multiparametric potential function. As an illustration of the method proposed he considers an example of a galactic-type potential in the form of power series with respect to the parameter and Vinti's problem in artificial satellite theory.