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Relative Equilibria in the 3-Dimensional Curved $n$-Body Problem
 
Florin Diacu University of Victoria, Victoria, B.C., Canada
Relative Equilibria in the 3-Dimensional Curved $n$-Body Problem
eBook ISBN:  978-1-4704-1483-2
Product Code:  MEMO/228/1071.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
Relative Equilibria in the 3-Dimensional Curved $n$-Body Problem
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Relative Equilibria in the 3-Dimensional Curved $n$-Body Problem
Florin Diacu University of Victoria, Victoria, B.C., Canada
eBook ISBN:  978-1-4704-1483-2
Product Code:  MEMO/228/1071.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2282014; 80 pp
    MSC: Primary 70; Secondary 34; 37;

    The author considers the \(3\)-dimensional gravitational \(n\)-body problem, \(n\ge 2\), in spaces of constant Gaussian curvature \(\kappa\ne 0\), i.e. on spheres \({\mathbb S}_\kappa^3\), for \(\kappa>0\), and on hyperbolic manifolds \({\mathbb H}_\kappa^3\), for \(\kappa<0\). His goal is to define and study relative equilibria, which are orbits whose mutual distances remain constant in time. He also briefly discusses the issue of singularities in order to avoid impossible configurations. He derives the equations of motion and defines six classes of relative equilibria, which follow naturally from the geometric properties of \({\mathbb S}_\kappa^3\) and \({\mathbb H}_\kappa^3\). Then he proves several criteria, each expressing the conditions for the existence of a certain class of relative equilibria, some of which have a simple rotation, whereas others perform a double rotation, and he describes their qualitative behaviour.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. BACKGROUND AND EQUATIONS OF MOTION
    • 3. ISOMETRIES AND RELATIVE EQUILIBRIA
    • 4. CRITERIA AND QUALITATIVE BEHAVIOUR
    • 5. EXAMPLES
    • 6. CONCLUSIONS
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2282014; 80 pp
MSC: Primary 70; Secondary 34; 37;

The author considers the \(3\)-dimensional gravitational \(n\)-body problem, \(n\ge 2\), in spaces of constant Gaussian curvature \(\kappa\ne 0\), i.e. on spheres \({\mathbb S}_\kappa^3\), for \(\kappa>0\), and on hyperbolic manifolds \({\mathbb H}_\kappa^3\), for \(\kappa<0\). His goal is to define and study relative equilibria, which are orbits whose mutual distances remain constant in time. He also briefly discusses the issue of singularities in order to avoid impossible configurations. He derives the equations of motion and defines six classes of relative equilibria, which follow naturally from the geometric properties of \({\mathbb S}_\kappa^3\) and \({\mathbb H}_\kappa^3\). Then he proves several criteria, each expressing the conditions for the existence of a certain class of relative equilibria, some of which have a simple rotation, whereas others perform a double rotation, and he describes their qualitative behaviour.

  • Chapters
  • 1. Introduction
  • 2. BACKGROUND AND EQUATIONS OF MOTION
  • 3. ISOMETRIES AND RELATIVE EQUILIBRIA
  • 4. CRITERIA AND QUALITATIVE BEHAVIOUR
  • 5. EXAMPLES
  • 6. CONCLUSIONS
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.