The Resource Relative equilibria of the curved N-body problem, Florin Diacu

# Relative equilibria of the curved N-body problem, Florin Diacu Resource Information The item Relative equilibria of the curved N-body problem, Florin Diacu represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.

Label
Relative equilibria of the curved N-body problem
Title
Relative equilibria of the curved N-body problem
Statement of responsibility
Florin Diacu
Creator
Subject
Language
eng
Summary
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
Member of
GW5XE
1959-2018
Diacu, Florin
Dewey number
530.14/4
Illustrations
portraits
Index
index present
LC call number
QA378
LC item number
.D53 2012
Literary form
non fiction
Nature of contents
• dictionaries
• bibliography
Series statement
Atlantis studies in dynamical systems
Series volume
v. 1
• Many-body problem
• Differential equations
• Celestial mechanics
• Mathematical Concepts
• Mathematics
• Mechanics
• Gravitation
• Physics
• SCIENCE
• Celestial mechanics
• Differential equations
• Many-body problem
Label
Relative equilibria of the curved N-body problem, Florin Diacu
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
• cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
• txt
Content type MARC source
rdacontent
Contents
• Relative Equilibria (RE)
• Fixed Points (FP)
• pt. 3.
• Criteria and Qualitative Behavior
• Existence Criteria
• Qualitative Behavior
• pt. 4.
• Examples
• Positive Elliptic RE
• Positive Elliptic-Elliptic RE
• Introduction
• Negative RE
• pt. 5.
• The 2-dimensional case
• Polygonal RE
• Lagrangian and Eulerian RE
• Saari's Conjecture
• pt. 1.
• Background and Equations of Motion
• Preliminary Developments
• Equations of motion
• pt. 2.
• Isometries and Relative Equilibria
• Isometric Rotations
Control code
808632285
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9781283634489
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
• c
Other control number
10.2991/978-94-91216-68-8
Other physical details
portraits.
394693
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)808632285
Label
Relative equilibria of the curved N-body problem, Florin Diacu
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
• cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
• txt
Content type MARC source
rdacontent
Contents
• Relative Equilibria (RE)
• Fixed Points (FP)
• pt. 3.
• Criteria and Qualitative Behavior
• Existence Criteria
• Qualitative Behavior
• pt. 4.
• Examples
• Positive Elliptic RE
• Positive Elliptic-Elliptic RE
• Introduction
• Negative RE
• pt. 5.
• The 2-dimensional case
• Polygonal RE
• Lagrangian and Eulerian RE
• Saari's Conjecture
• pt. 1.
• Background and Equations of Motion
• Preliminary Developments
• Equations of motion
• pt. 2.
• Isometries and Relative Equilibria
• Isometric Rotations
Control code
808632285
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9781283634489
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
• c
Other control number
10.2991/978-94-91216-68-8
Other physical details
portraits.
394693
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)808632285

#### Library Locations

• Ellis Library
1020 Lowry Street, Columbia, MO, 65201, US
38.944491 -92.326012