New Methods of Celestial Mechanics, Periodic and Asymptotic Solutions, Approximations By Series, & Integral Invariants and Asymptotic Properties of Certain Solutions, 3 Volumes

Poincare, Henri

ISBN 10: 1563961172 / ISBN 13: 9781563961175

Verlag: Amer Inst of Physics, Woodbury, New York, U.S.A., 1992

Beschreibung

This is a fine, three volume set in red cloth with gold stamping, no DJs. A smudge to the bottom edge of volume 2, otherwise a like new set. Obviously unread. MEDIA SHIPPING ONLY.

Bestandsnummer des Verkäufers 034170

Bibliografische Details

• Titel: New Methods of Celestial Mechanics, Periodic and Asymptotic Solutions, Approximations By Series, & Integral Invariants and Asymptotic Properties of Certain Solutions, 3 Volumes
• Verlag: Amer Inst of Physics, Woodbury, New York, U.S.A.
• Erscheinungsjahr: 1992
• Sprache: Englisch
• ISBN-10: 1563961172
• ISBN-13: 9781563961175
• Einband: Cloth
• Auflage: First Thus
• Zustand: Fine
• Zustand des Schutzumschlags: No Jacket

Über diesen Titel

Inhaltsangabe

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. Contents: Volume I: Periodic and asymptotic solutions: 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 II: Approximations by series: 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 III: Integral invariants and asymptotic properties of certain solutions: 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.