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Relative Equilibria of the Curved N-Body Problem (Record no. 24212)

000 -LEADER
fixed length control field 04034nam a22004455i 4500
003 - CONTROL NUMBER IDENTIFIER
control field OSt
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20140310151501.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr nn 008mamaa
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 120817s2012 fr | s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9789491216688
978-94-91216-68-8
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA313
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 515.39
Edition number 23
Classification number 515.48
Edition number 23
264 #1 -
-- Paris :
-- Atlantis Press :
-- Imprint: Atlantis Press,
-- 2012.
912 ## -
-- ZDB-2-SMA
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Diacu, Florin.
Relator term author.
245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE
Title Relative Equilibria of the Curved N-Body Problem
Medium [electronic resource] /
Statement of responsibility, etc by Florin Diacu.
300 ## - PHYSICAL DESCRIPTION
Extent XIV, 143 p. 9 illus.
Other physical details online resource.
440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE
Title Atlantis Series in Dynamical Systems ;
Volume number/sequential designation 1
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Introduction -- Preliminary developments -- Equations of motion -- Isometric rotations -- Relative equilibria (RE) -- Fixed Points (FP) -- Existence criteria -- Qualitative behavior -- Positive elliptic RE -- Positive elliptic-elliptic RE -- Negative RE -- Polygonal RE -- Lagrangian and Eulerian RE -- Saari’s conjecture.
520 ## - SUMMARY, ETC.
Summary, etc The guiding light of this monograph 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 monograph provides a mathematical proof that, for distances of the order of 10 AU, space is Euclidean. This result is, of course, not 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 non-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 Janos 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, non-Euclidean geometry, geometric topology, Lie groups, and the theory of polytopes.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics.
Topical term or geographic name as entry element Differentiable dynamical systems.
Topical term or geographic name as entry element Differential Equations.
Topical term or geographic name as entry element Mathematics.
Topical term or geographic name as entry element Dynamical Systems and Ergodic Theory.
Topical term or geographic name as entry element Ordinary Differential Equations.
Topical term or geographic name as entry element Mathematics, general.
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title Springer eBooks
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Printed edition:
International Standard Book Number 9789491216671
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier http://dx.doi.org/10.2991/978-94-91216-68-8
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Item type E-Book
Copies
Price effective from Permanent location Date last seen Not for loan Date acquired Source of classification or shelving scheme Koha item type Damaged status Lost status Withdrawn status Current location Full call number
2014-04-10AUM Main Library2014-04-10 2014-04-10 E-Book   AUM Main Library515.39
Languages: 
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العربية