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Collisions, Rings, and Other Newtonian $N$-Body Problems

Donald G. Saari University of California, Irvine, CA
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-0-8218-3250-9
Product Code: CBMS/104
235 pp
List Price: $52.00 Individual Price:$41.60
Electronic ISBN: 978-1-4704-2464-0
Product Code: CBMS/104.E
235 pp
List Price: $49.00 Individual Price:$39.20
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List Price: $78.00 Click above image for expanded view Collisions, Rings, and Other Newtonian$N$-Body Problems Donald G. Saari University of California, Irvine, CA A co-publication of the AMS and CBMS Available Formats:  Softcover ISBN: 978-0-8218-3250-9 Product Code: CBMS/104 235 pp  List Price:$52.00 Individual Price: $41.60  Electronic ISBN: 978-1-4704-2464-0 Product Code: CBMS/104.E 235 pp  List Price:$49.00 Individual Price: $39.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$78.00
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 1042005
MSC: Primary 70;

Written by well-known expert Donald Saari, this book is directed toward readers who want to learn about the Newtonian $N$-body problem. It is also intended for students and experts who are interested in new expositions of past results in this area, previously unpublished research conclusions, and new research problems.

Professor Saari has written the book for a broad audience, including readers with no previous knowledge about this fascinating area. He begins each chapter with introductory material motivated by unanswered research questions. He then includes some history, discussions intended to develop intuition, descriptions of open problems, and examples taken from real problems in astronomy.

The first chapter starts with simple explanations of the apparent "looping" orbit of Mars and the unexpected "Sunrise, Sunset" behavior as viewed from Mercury and then leads up to the unexplained and weird dynamics exhibited by Saturn's F-ring. The second chapter, which introduces a way to decompose the velocity of the system, is motivated by a seemingly easy but unanswered conjecture involving the dynamics of the system when the system's diameter is a constant. The third chapter, which describes questions about the structure of the rings of Saturn, introduces new and surprisingly simple ways to find configurations of the particles that are "central" to any discussion of the $N$-body problem. The fourth chapter analyzes collisions, and the last chapter discusses the likelihood of collisions and other events.

The book is suitable for graduate students and researchers interested in celestial mechanics.

Graduate students and research mathematicians interested in celestial mechanics.

• Chapters
• 1. Introduction
• 2. Central configurations
• 3. Finding central configurations
• 4. Collisions–Both real and imaginary
• 5. How likely is it?

• Reviews

• The book can be useful for readers who are interested in learning celestial mechanics and particularly the Newtonian N-body problem as well as for students, postgraduate students and experts in this area who are interested in new expositions of past results, previously unpublished research conclusions, and new research problems.

Zentralblatt MATH
• Request Review Copy
Volume: 1042005
MSC: Primary 70;

Written by well-known expert Donald Saari, this book is directed toward readers who want to learn about the Newtonian $N$-body problem. It is also intended for students and experts who are interested in new expositions of past results in this area, previously unpublished research conclusions, and new research problems.

Professor Saari has written the book for a broad audience, including readers with no previous knowledge about this fascinating area. He begins each chapter with introductory material motivated by unanswered research questions. He then includes some history, discussions intended to develop intuition, descriptions of open problems, and examples taken from real problems in astronomy.

The first chapter starts with simple explanations of the apparent "looping" orbit of Mars and the unexpected "Sunrise, Sunset" behavior as viewed from Mercury and then leads up to the unexplained and weird dynamics exhibited by Saturn's F-ring. The second chapter, which introduces a way to decompose the velocity of the system, is motivated by a seemingly easy but unanswered conjecture involving the dynamics of the system when the system's diameter is a constant. The third chapter, which describes questions about the structure of the rings of Saturn, introduces new and surprisingly simple ways to find configurations of the particles that are "central" to any discussion of the $N$-body problem. The fourth chapter analyzes collisions, and the last chapter discusses the likelihood of collisions and other events.

The book is suitable for graduate students and researchers interested in celestial mechanics.