Andoyer construction for Hill and Delaunay variables

TL;DR

This paper explores the Andoyer construction method, demonstrating its ability to derive Hill and Delaunay variables for celestial mechanics without relying on generating functions, thus offering a unified approach.

Contribution

The paper introduces a novel application of the Andoyer construction to derive Hill and Delaunay variables, simplifying their canonical formulation.

Findings

Andoyer construction can derive Hill variables for the Kepler problem.

It can also predict Delaunay variables with inherent canonicity.

The method eliminates the need for generating functions in these derivations.

Abstract

Andoyer variables are well known for the study of rotational dynamics. These variables were derived by Andoyer through a procedure that can be also used to obtain the Hill variables of the Kepler problem. Andoyer construction can also forecast the Delaunay variables which canonicity is then obtained without the use of a generating function.