Kam Stability And Celestial Mechanics
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KAM Stability and Celestial Mechanics
Author: Alessandra Celletti
language: en
Publisher: American Mathematical Soc.
Release Date: 2007
KAM theory is a powerful tool apt to prove perpetual stability in Hamiltonian systems, which are a perturbation of integrable ones. The smallness requirements for its applicability are well known to be extremely stringent. A long standing problem, in this context, is the application of KAM theory to physical systems for observable values of the perturbation parameters. The authors consider the Restricted, Circular, Planar, Three-Body Problem (RCP3BP), i.e., the problem of studying the planar motions of a small body subject to the gravitational attraction of two primary bodies revolving on circular Keplerian orbits (which are assumed not to be influenced by the small body).
Stability and Chaos in Celestial Mechanics
Author: Alessandra Celletti
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-03-10
This overview of classical celestial mechanics focuses the interplay with dynamical systems. Paradigmatic models introduce key concepts – order, chaos, invariant curves and cantori – followed by the investigation of dynamical systems with numerical methods.
Periodic, Quasi-Periodic and Chaotic Motions in Celestial Mechanics: Theory and Applications
Author: Alessandra Celletti
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-02-02
The book provides the most recent advances of Celestial Mechanics, as provided by high-level scientists working in this field. It covers theoretical investigations as well as applications to concrete problems. Outstanding review papers are included in the book and they introduce the reader to leading subjects, like the variational approaches to find periodic orbits and the space debris polluting the circumterrestrial space.