Integrable Systems in Celestial Mechanics
Language: English
Published by Birkhäuser, 2008
- Hardcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
AbeBooks seller since August 14, 2006
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Add to basketItem description from seller
Druck auf Anfrage Neuware - Printed after ordering - Direct involvement with the subject area of the present work dates from my years with NASA at its Electronics Research Center (ERC) in Cambridge, M- sachusetts, in the 1960s. However, my approach to the problems of mathem- ical physics had been shaped earlier in my time as a graduate student in the Mathematics Department at MIT. The passage of time tends merely to further enhance my appreciation of that graduate study program, where I had the b- e t of the intensive courses from Norman Levinson, C.-C. Lin, Jurgen Moser, and Eric Reissner. In the case of Reissner, my years as research assistant were a formative apprenticeship - one could say on the 'shop- oor'. The stimulus to organize my convictions in book form came from my friends at Birkh auser Boston, and I wish to thank Ann Kostant for providing me with the opportunity and support in producing it; a special thanks goes to Edwin Beschler, formerly of Birkh auser, for his consistent encouragement over the years. In the course of writing, I had the good-humored support and invaluable help from my one-time teacher and long-time friend, Vincent Hart. He read each chapter as it was written and his sharp eye picked up my many slips and errors. More signi cantly, his persistent questioning on the original form of Chapter 3 forced me to address all parameter ranges and provide solution forms to cover all possibilities for the case of negative energy.…
Seller Inventory # 9780817640965
- Title
- Integrable Systems in Celestial Mechanics
- Author
- Diarmuid Ó'Mathúna
- Publisher
- Birkhäuser
- Publication year
- 2008
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 0817640967
- ISBN 13
- 9780817640965
- Item weight
- 541 grams
- Dimensions
- 241x160x19 mm
- Series
- Book 17 of 37: Progress in Mathematical Physics
Shows that exact solutions to the Kepler (two-body), the Euler (two-fixed center), and the Vinti (earth-satellite) problems can all be put in a form that admits the general representation of the orbits and follows a definite shared pattern
Includes a full analysis of the planar Euler problem via a clear generalization of the form of the solution in the Kepler case
Original insights that have hithertofore not appeared in book form
"Synopsis" may belong to another edition of this title.
From the Back Cover
This work presents a unified treatment of three important integrable problems relevant to both Celestial and Quantum Mechanics. Under discussion are the Kepler (two-body) problem and the Euler (two-fixed 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 (Earth-satellite) 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 Earth-satellite (Vinti) problem.
Key features:
* Highlights shared features in the unified treatment of the Kepler, Euler, and Vinti problems
* Raises challenges in analysis and astronomy, placing this trio of problems in the modern context
* Includes a full analysis of the planar Euler problem
* Highlights the complex and surprising orbit patterns that arise from the Euler problem
* Provides a detailed analysis and solution for the Earth-satellite 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.
"About the title" may belong to another edition of this title.
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