New Methods of Celestial Mechanics VOLUME 2 Approximations By Series (History of Modern Physics and Astronomy: Vol 13)

Poincare, Henri

ISBN 10: 1563961156 / ISBN 13: 9781563961151

Published by American Institute of Physics, Harvard University, 1993

About this Item

VOLUME 2. Pages 317 - 722 + notes pages. No dustjacket. Brown hardback binding, light marks to covers, spine has a light damp-marked area, light wear to spine-ends and boards' corners. Pages clean as though lightly used but not very well stored.

Seller Inventory # 067059

Bibliographic Details

• Title: New Methods of Celestial Mechanics VOLUME 2 Approximations By Series (History of Modern Physics and Astronomy: Vol 13)
• Publisher: American Institute of Physics, Harvard University
• Publication Date: 1993
• Language: English
• ISBN 10: 1563961156
• ISBN 13: 9781563961151
• Binding: Hardcover
• Condition: Fair
• Dust Jacket Condition: No Dustjacket

About this title

Synopsis

Edited by Daniel Goroff, Harvard University This English-language edition of Poincare's landmark work is of interest not only to historians of science, but also to mathematicians. Beginning from an investigation of the three-body problem of Newtonian mechanics, Poincare lays the foundations of the qualitative solutions of differential equations. To investigate the long-unsolved problem of the stability of the Solar System, Poincare invented a number of new techniques including canonical transformations, asymptotic series expansions, and integral invariants. These "new methods" are even now finding applications in chaos and other contemporary disciplines. Volume Periodic and asymptotic Introduction by Daniel Goroff. Generalities and the Jacobi method. Series integration. Periodic solutions. Characteristic exponents. Nonexistence of uniform integrals. Approximate development of the perturbative function. Asymptotic solutions. Volume Approximations by Formal calculus. Methods of Newcomb and Lindstedt. Application to the study of secular variations. Application to the three-body problem. Application to orbits. Divergence of the Lindstedt series. Direct calculation of the series. Other methods of direct calculation. Gylden methods. Case of linear equations. Bohlin methods. Bohlin series. Extension of the Bohlin method. Volume Integral invariants and asymptotic properties of certain Integral invariants. Formation of invariants. Use of integral invariants. Integral invariants and asymptotic solutions. Poisson stability. Theory of consequents. Periodic solutions of the second kind. Different forms of the principle of least action.