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 complexa "and surprising orbita "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) andresearchers 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.
General
| Imprint: |
Birkhauser Boston
|
| Country of origin: |
United States |
| Series: |
Progress in Mathematical Physics, 51 |
| Release date: |
August 2008 |
| First published: |
June 2008 |
| Authors: |
Diarmuid O Math una
|
| Dimensions: |
235 x 155 x 15mm (L x W x T) |
| Format: |
Hardcover
|
| Pages: |
234 |
| Edition: |
2008 ed. |
| ISBN-13: |
978-0-8176-4096-5 |
| Categories: |
Books >
Science & Mathematics >
Astronomy, space & time >
General
|
| LSN: |
0-8176-4096-7 |
| Barcode: |
9780817640965 |
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