Springer celebrates 175 years of publishing excellence! Join us >>

Progress in Mathematical Physics

Integrable Systems in Celestial Mechanics

Authors: Ó'Mathúna, Diarmuid

  • Presents three historical and important problems of celestial mechanics in a modern context
  • Provides as unified treatment of three problems relevant to both celestial and quantum mechanics
see more benefits

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-0-8176-4595-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-0-8176-4096-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (7 chapters)

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-0-8176-4595-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-0-8176-4096-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Integrable Systems in Celestial Mechanics
Authors
Series Title
Progress in Mathematical Physics
Series Volume
51
Copyright
2008
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4595-3
DOI
10.1007/978-0-8176-4595-3
Hardcover ISBN
978-0-8176-4096-5
Series ISSN
1544-9998
Edition Number
1
Number of Pages
X, 234
Number of Illustrations and Tables
24 b/w illustrations
Topics