Integrable systems in celestial mechanics
Resource Information
The work Integrable systems in celestial mechanics represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Integrable systems in celestial mechanics
Resource Information
The work Integrable systems in celestial mechanics represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Integrable systems in celestial mechanics
 Statement of responsibility
 Diarmuid Ó Mathúna
 Language
 eng
 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. 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 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
 Cataloging source
 GW5XE
 Dewey number
 521
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QB351
 LC item number
 .O43 2008eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Progress in mathematical physics
 Series volume
 v. 51
Context
Context of Integrable systems in celestial mechanicsWork of
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