Theory of Orbits

This textbook treats celestial mechanics as well as stellar dynamics from the common point of view of orbit theory making use of concepts and techniques from modern geometric mechanics. The book is meant for students in astronomy and physics with a knowledge of calculus and differential geometry.

First textbook which treats celestial mechanics and stellar dynamics at the same level of presentation Both fields are extremely active for theoretical as well as observational reasons Includes supplementary material: sn.pub/extras

Texte du rabat

This textbook treats Celestial Mechanics as well as Stellar Dynamics from the common point of view of orbit theory making use of the concepts and techniques from modern geometric mechanics. It starts with elementary Newtonian Mechanics and ends with the dynamics of chaotic motions. The book is meant for students in astronomy and physics alike. Prerequisite is a physicist's knowledge of calculus and differential geometry. Volume 1 begins with classical mechanics and a thorough treatment of the 2-body problem, including regularization, followed by an introduction to the N-body problem with particular attention given to the virial theorem. Then the authors discuss all important non-perturbative aspects of the 3-body problem. A final chapter deals with integrability of Hamilton-Jacobi systems.

Résumé
From the reviews
"The book is ... didactically written and contains topics from classical to most modern ones, treated rigorously by indicating where complete proofs are to be found."
Zentralblatt für Mathematik, 1999

Contenu
The Theory of Orbits from Epicycles to Chaos.- 1. Dynamics and Dynamical Systems Quod Satis.- 2. The Two-Body Problem.- 3. The N-Body Problem.- 4. The Three-Body Problem.- 5. Orbits in Given Potentials.- Mathematical Appendix.- A.1 Spherical Trigonometry.- A.2 Curvilinear Coordinate Systems.- A.3 Riemannian Geometry.- Bibliographical Notes.- Name Index.