Methods of algebraic manipulation in perturbation theory

Abstract

We give a short introduction to the methods of representing polynomial and trigonometric series that are often used in Celestial Mechanics. A few applications are also illustrated.

37 pages, 10 figures

References in corpus (2)

• On the stability of the secular evolution of the planar Sun-Jupiter-Saturn-Uranus system
• The Piranha algebraic manipulator

Cited by in corpus (5)

• Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories
• Elliptic tori in FPU non-linear chains with a small number of nodes
• Librational KAM tori in the secular dynamics of the $\upsilon$ Andromedæ planetary system
• Normal form for lower dimensional elliptic tori in Hamiltonian systems
• Existence proof of librational invariant tori in an averaged model of HD60532 planetary system