The Resource Integrable systems in celestial mechanics, Diarmuid Ó Mathúna
Integrable systems in celestial mechanics, Diarmuid Ó Mathúna
Resource Information
The item Integrable systems in celestial mechanics, Diarmuid Ó Mathúna represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Integrable systems in celestial mechanics, Diarmuid Ó Mathúna represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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
 Language
 eng
 Extent
 1 online resource (x, 234 pages)
 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
 Isbn
 9780817645953
 Label
 Integrable systems in celestial mechanics
 Title
 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
 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
 Twobody problem
 SCIENCE
 Celestial mechanics
 Twobody problem
 Himmelsmechanik
 Integrables System
 Label
 Integrable systems in celestial mechanics, Diarmuid Ó Mathúna
 Bibliography note
 Includes bibliographical references (pages 227230) 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 (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
 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
 10.1007/9780817645953
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9780817640965
 Specific material designation
 remote
 System control number
 (OCoLC)314371862
 Label
 Integrable systems in celestial mechanics, Diarmuid Ó Mathúna
 Bibliography note
 Includes bibliographical references (pages 227230) 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 (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
 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
 10.1007/9780817645953
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9780817640965
 Specific material designation
 remote
 System control number
 (OCoLC)314371862
Library Links
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Integrablesystemsincelestialmechanics/m3K7jXZPhtw/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Integrablesystemsincelestialmechanics/m3K7jXZPhtw/">Integrable systems in celestial mechanics, Diarmuid Ó Mathúna</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item Integrable systems in celestial mechanics, Diarmuid Ó Mathúna
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Integrablesystemsincelestialmechanics/m3K7jXZPhtw/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Integrablesystemsincelestialmechanics/m3K7jXZPhtw/">Integrable systems in celestial mechanics, Diarmuid Ó Mathúna</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>