Integrable systems in celestial mechanics
 Responsibility
 Diarmuid Ó Mathúna.
 Language
 English.
 Imprint
 Boston : Birkhäuser, c2008.
 Physical description
 x, 234 p. : ill. ; 25 cm.
 Series
 Progress in mathematical physics v. 51.
Access
Available online
 site.ebrary.com ebrary
 dx.doi.org SpringerLink
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Call number  Status 

QB351 .O43 2008  Available 
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Creators/Contributors
 Author/Creator
 Ó Mathúna, Diarmuid.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [227]230) and index.
 Contents

 General Introduction. The Kepler Problem (TwoBody Problem): the central Newtonian potential. Bernoulli solution. Features of the central Newtonian potential. The NonCentral Newtonian Potential. The Euler problem: two fixed centers of attraction. The Vinti problem: earthsatellite theory. Implications for perturbation theories. Relativistic context. Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 This work presents a unified treatment of three important integrable problems relevant to both Celestial and Quantum Mechanics. Under discussion are the Kepler (twobody) problem and the Euler (twofixed center) problem, the latter being the more complex and more instructive, as it exhibits a richer and more varied solution structure. Further, because of the interesting investigations by the 20th century mathematical physicist J.P. Vinti, the Euler problem is now recognized as being intimately linked to the Vinti (Earthsatellite) problem. Here the analysis of these problems is shown to follow a definite shared pattern yielding exact forms for the solutions. A central feature is the detailed treatment of the planar Euler problem where the solutions are expressed in terms of Jacobian elliptic functions, yielding analytic representations for the orbits over the entire parameter range. This exhibits the rich and varied solution patterns that emerge in the Euler problem, which are illustrated in the appendix. A comparably detailed analysis is performed for the Earthsatellite (Vinti) problem. This book highlights shared features in the unified treatment of the Kepler, Euler, and Vinti problems. It raises challenges in analysis and astronomy, placing this trio of problems in the modern context. It includes a full analysis of the planar Euler problem. It highlights the complex  and surprising orbit  patterns that arise from the Euler problem. It provides a detailed analysis and solution for the Earthsatellite problem. The analysis and results in this work will be of interest to graduate students in mathematics and physics (including physical chemistry) and researchers concerned with the general areas of dynamical systems, statistical mechanics, and mathematical physics and has direct application to celestial mechanics, astronomy, orbital mechanics, and aerospace engineering.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2008
 Series
 Progress in mathematical physics ; v. 51
 ISBN
 9780817640965 (cloth)
 0817640967 (cloth)
 9780817645953 (ebook)
 0817645950 (ebook)