Perturbation theory and canonical coordinates in celestial mechanics

TL;DR

This paper reviews advances in applying perturbation theory and canonical coordinates to celestial mechanics, highlighting the development of methods that leverage invariance and near-integrability for better understanding planetary systems.

Contribution

It provides a comprehensive review of recent progress in symplectic methods and coordinate transformations in celestial mechanics, building on Arnold's foundational work.

Findings

Enhanced symplectic assessment techniques

Development of coordinates respecting invariance and near-integrability

Progress in applying KAM theory to planetary problems

Abstract

KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by V.I.Arnold in the 60s who worked out a theorem, that he named the Fundamental Theorem (FT), especially designed for the planetary problem. However, FT could be really used at that purpose only when, about 50 years later, a set of coordinates constructively taking the invariance by rotation and close-to-integrability into account was used. Since then, some progress has been done in the symplectic assessment of the problem, and here we review such results.