Finiteness of relative equilibria in the planar generalized \(N\)-body problem with fixed subconfigurations

DOI10.3934/jgm.2015.7.35zbMath1367.70027OpenAlexW2327631698MaRDI QIDQ888751

Marshall Hampton, Anders Nedergaard Jensen

Publication date: 2 November 2015

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jgm.2015.7.35

zbMATH Keywords

relative equilibriavortices\(N\)-body problemcelestial mechanicscentral configurations

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Equilibria and periodic trajectories for nonlinear problems in mechanics (70K42) Celestial mechanics (70F15) (n)-body problems (70F10) Algebraic geometry methods for problems in mechanics (70G55)

Related Items (7)

Finiteness of Spatial Central Configurations with Fixed Subconfigurations ⋮ On intersections and stable intersections of tropical hypersurfaces ⋮ Unnamed Item ⋮ Stacked central configurations in the 5-vortex problem ⋮ Planar \(N\)-body central configurations with a homogeneous potential ⋮ Pruning Algorithms for Pretropisms of Newton Polytopes ⋮ Equilateral chains and cyclic central configurations of the planar five-body problem

Uses Software

• Gfan

Cites Work

• Finiteness of spatial central configurations in the five-body problem
• Finiteness of central configurations of five bodies in the plane
• Central configurations with many small masses
• Finiteness of relative equilibria of the four-body problem
• Relative equilibria with clusters of small masses
• The \(n\)-body problem and mutual distances
• Mathematical problems for the next century
• A continuum of relative equilibria in the five-body problem
• On central configurations
• Finiteness of kite relative equilibria in the five-vortex and five-body problems
• Finiteness in the planar restricted four-body problem
• Generic Finiteness for Dziobek Configurations
• Finiteness of stationary configurations of the four-vortex problem
• The number of planar central configurations is finite when $N-1$ mass positions are fixed
• The tropical Grassmannian
• Distribution of Points in n-Space
• Unnamed Item

This page was built for publication: Finiteness of relative equilibria in the planar generalized \(N\)-body problem with fixed subconfigurations