Solution to the main problem of the artificial satellite by reverse normalization

TL;DR

This paper proposes a novel normalization approach to simplify the analysis of artificial satellite dynamics, eliminating the need for Hamiltonian simplification and enabling higher-order perturbation solutions.

Contribution

It introduces a new normalization method that bypasses traditional Hamiltonian simplification, improving the efficiency and accuracy of satellite orbit analysis.

Findings

Decoupling orbital plane motion enhances perturbation solution order.

The new method simplifies the analytical solution process.

Higher-order solutions are more efficiently computed with this approach.

Abstract

The non-linearities of the dynamics of Earth artificial satellites are encapsulated by two formal integrals that are customarily computed by perturbation methods. Standard procedures begin with a Hamiltonian simplification that removes non-essential short-period terms from the Geopotential, and follow with the removal of both short- and long-period terms by means of two different canonical transformations that can be carried out in either order. We depart from the tradition and proceed by standard normalization to show that the Hamiltonian simplification part is dispensable. Decoupling first the motion of the orbital plane from the in-plane motion reveals as a feasible strategy to reach higher orders of the perturbation solution, which, besides, permits an efficient evaluation of the long series that comprise the analytical solution.