The Symmetric Anomaly and its Computational Application

For the equation of oscillations of a satellite in the plane of its elliptic orbit (the Beletskii equation), we introduce a new anomaly of the position of a satellite on the orbit, which we call the symmetric anomaly, and which in the first approximation behaves as a regularizing change of the independent variable in the neighborhood of all singularities of the equation. The effectiveness of the symmetric anomaly for computation of the generalized periodic solutions to the Beletskii equation is demonstrated when eccentricity |e| \to 1. It is shown that if the symmetric anomaly is used, then all characteristics of the generalized periodic solutions to the Beletskii equation have the same asymptotics for μ →+\infty , which does not depend on the value of the eccentricity e ∈ [-1,1].