Coverart for item
The Resource Integrable systems in celestial mechanics, Diarmuid Ó Mathúna

Integrable systems in celestial mechanics, Diarmuid Ó Mathúna

Label
Integrable systems in celestial mechanics
Title
Integrable systems in celestial mechanics
Statement of responsibility
Diarmuid Ó Mathúna
Creator
Subject
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 (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
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Ó Mathúna, Diarmuid
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
http://library.link/vocab/subjectName
  • Celestial mechanics
  • Two-body problem
  • SCIENCE
  • Celestial mechanics
  • Two-body problem
  • Himmelsmechanik
  • Integrables System
Label
Integrable systems in celestial mechanics, Diarmuid Ó Mathúna
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 227-230) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
General Introduction -- The Kepler Problem (Two-Body Problem): the central Newtonian potential -- Bernoulli solution -- Features of the central Newtonian potential -- The Non-Central Newtonian Potential -- The Euler problem: two fixed centers of attraction -- The Vinti problem: earth-satellite theory -- Implications for perturbation theories -- Relativistic context -- Index
Control code
314371862
Dimensions
unknown
Extent
1 online resource (x, 234 pages)
Form of item
online
Isbn
9780817645953
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-8176-4595-3
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-0-8176-4096-5
Specific material designation
remote
System control number
(OCoLC)314371862
Label
Integrable systems in celestial mechanics, Diarmuid Ó Mathúna
Publication
Bibliography note
Includes bibliographical references (pages 227-230) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
General Introduction -- The Kepler Problem (Two-Body Problem): the central Newtonian potential -- Bernoulli solution -- Features of the central Newtonian potential -- The Non-Central Newtonian Potential -- The Euler problem: two fixed centers of attraction -- The Vinti problem: earth-satellite theory -- Implications for perturbation theories -- Relativistic context -- Index
Control code
314371862
Dimensions
unknown
Extent
1 online resource (x, 234 pages)
Form of item
online
Isbn
9780817645953
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-8176-4595-3
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-0-8176-4096-5
Specific material designation
remote
System control number
(OCoLC)314371862

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