Brouwer's satellite solution redux

TL;DR

This paper revisits Brouwer's satellite solution, demonstrating that a complete Hamiltonian reduction can be achieved through a single canonical transformation in Poincaré's style, simplifying the traditional multi-step process.

Contribution

It shows that Brouwer's solution can be obtained via a single canonical transformation, contrasting with the conventional multi-step reduction methods.

Findings

Complete Hamiltonian reduction achieved with one canonical transformation.

Simplifies Brouwer's satellite solution methodology.

Highlights advantages of Poincaré's approach over von Zeipel's sequence.

Abstract

Brouwer's solution to the artificial satellite problem is revisited to show that the complete Hamiltonian reduction is rather achieved in the plain Poincar\'e's style, through a single canonical transformation, than using a sequence of partial reductions based on von Zeipel's alternative for dealing with perturbed degenerate Hamiltonian systems.