Relative Equilibria of the Curved N-Body Problem

• Main Author: Diacu, Florin (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Paris : Atlantis Press : Imprint: Atlantis Press, 2012.
• Series: Atlantis Series in Dynamical Systems ; 1
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Differential equations.; Dynamical Systems and Ergodic Theory.; Ordinary Differential Equations.; Mathematics, general.

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...

Table of Contents:

• 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.