eBay |

# Relative Equilibria of the Curved N-Body Problem by Florin Diacu (Hardback, 2012)

Be the first to write a review.

OUR TOP PICK

## $164.00

List price $193.99 Save 15%

Quantity

1 available

Condition

Brand new

Sold by

simplybestprices-10to20dayshipping (239116)98.3% positive Feedback

Returns

30 days money back

Buyer pays return postage

## All listings for this product

## Save on Non-Fiction Books

### NEW Codex Seraphinianus By Luigi Serafini Hardcover Free Shipping

AU $132.35Trending at AU $138.02### Becoming a Supple Leopard: The Ultimate Guide to Resolving Pain, Preventing Inju

AU $62.03Trending at AU $72.32### Letters to You by Miriam Hathaway (Hardback, 2015)

AU $32.92Trending at AU $36.29### Easiest Piano Course Complete - Boxed Set (Books 1-4 with CD) Thompson

AU $37.69Trending at AU $47.53### 20/20 Diet by Phil McGraw (English) Hardcover Book

AU $30.90Trending at AU $31.80### Golden Universal Tarot Deck by Lo Scarabeo.

AU $30.58Trending at AU $37.06### The Big Book of Granny Squares 365 Crochet Motifs by Tracey Lord 9781620337110

AU $44.12Trending at AU $50.95

## About this product

### Description

- DescriptionThe guiding light of this mograph is a question easy to understand but difficult to answer: {What is the shape of the universe? In other words, how do we measure the shortest distance between two points of the physical space? Should we follow a straight line, as on a flat table, fly along a circle, as between Paris and New York, or take some other path, and if so, what would that path look like? If you accept that the model proposed here, which assumes a gravitational law extended to a universe of constant curvature, is a good approximation of the physical reality (and I will later outline a few arguments in this direction), then we can answer the above question for distances comparable to those of our solar system. More precisely, this mograph provides a mathematical proof that, for distances of the order of 10 AU, space is Euclidean. This result is, of course, t surprising for such small cosmic scales. Physicists take the flatness of space for granted in regions of that size. But it is good to finally have a mathematical confirmation in this sense. Our main goals, however, are mathematical. We will shed some light on the dynamics of N point masses that move in spaces of n-zero constant curvature according to an attraction law that naturally extends classical Newtonian gravitation beyond the flat (Euclidean) space. This extension is given by the cotangent potential, proposed by the German mathematician Ernest Schering in 1870. He was the first to obtain this analytic expression of a law suggested decades earlier for a 2-body problem in hyperbolic space by Jas Bolyai and, independently, by Nikolai Lobachevsky. As Newton's idea of gravitation was to introduce a force inversely proportional to the area of a sphere the same radius as the Euclidean distance between the bodies, Bolyai and Lobachevsky thought of a similar definition using the hyperbolic distance in hyperbolic space. The recent generalization we gave to the cotangent potential to any number N of bodies, led to the discovery of some interesting properties. This new research reveals certain connections among at least five branches of mathematics: classical dynamics, n-Euclidean geometry, geometric topology, Lie groups, and the theory of polytopes.

### Key Features

- Author(s)Florin Diacu
- PublisherAtlantis Press (Zeger Karssen)
- Date of Publication18/08/2012
- LanguageEnglish
- FormatHardback
- ISBN-109491216678
- ISBN-139789491216671
- SubjectMathematics
- Series TitleAtlantis Studies in Dynamical Systems
- Series Part/Volume Number1

### Publication Data

- Country of PublicationNetherlands
- ImprintAtlantis Press (Zeger Karssen)
- Content Notebiography

### Dimensions

- Weight405 g
- Width156 mm
- Height234 mm
- Spine11 mm

### Editorial Details

- Format DetailsLaminated cover

## Question & Answers

## Ask buyers and sellers about this product

Ask a questionThis item doesn't belong on this page.

Thanks, we'll look into this.