A computer-assisted proof of Saari’s conjecture for the planar three-body problem

DOI10.1090/S0002-9947-04-03527-5zbMath1079.70011WikidataQ123277040 ScholiaQ123277040MaRDI QIDQ4671894

Richard Moeckel

Publication date: 27 April 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

computational algebraconstant moment of inertia

Mathematics Subject Classification ID

Celestial mechanics (70F15) Dynamical systems in classical and celestial mechanics (37N05) (n)-body problems (70F10)

Related Items

Finiteness of relative equilibria of the four-body problem ⋮ On computer-assisted proving the existence of periodic and bounded orbits ⋮ Saari's conjecture is true for generic vector fields ⋮ Saari's conjecture for the restricted three-body problem ⋮ Constant locked inertia tensor trajectories for simple mechanical systems with symmetry ⋮ On the \(n\)-body problem on surfaces of revolution ⋮ Finiteness in the planar restricted four-body problem ⋮ The \(n\)-body problem in spaces of constant curvature. II: Singularities ⋮ Saari's homographic conjecture of the three-body problem ⋮ Saari's Conjecture for Elliptical Motions and Minimizing Solutions of the N-body Problem ⋮ Finiteness of stationary configurations of the four-vortex problem

Uses Software

• Mathematica
• PORTA

Cites Work

• Newton polytopes and the Bezout theorem
• The \(n\)-body problem and mutual distances
• Saari's conjecture for the planar three-body problem with equal masses
• Symmetric and regularized coordinates on the plane triple collision manifold
• Lectures on Polytopes
• A Symmetric Reduction of the Planar Three-Body Problem
• On a Symmetrical Canonical Reduction of the Problem of Three Bodies

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