Computing hyperbolic choreographies

DOI10.1134/S1560354716050038zbMath1402.70013arXiv1606.01850MaRDI QIDQ2520094

Hadrien Montanelli

Publication date: 13 December 2016

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.01850

zbMATH Keywords

Newton's methodtrigonometric interpolationquasi-Newton methodschoreographiescurved \(n\)-body problem

Mathematics Subject Classification ID

Celestial mechanics (70F15) (n)-body problems (70F10) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12)

Related Items (4)

Results on equality of masses for choreographic solutions of n-body problems ⋮ Reduction and relative equilibria for the two-body problem on spaces of constant curvature ⋮ A restricted four-body problem for the figure-eight choreography ⋮ Finding extremals of Lagrangian actions

Uses Software

• Chebfun

Cites Work

• Unnamed Item
• Relative equilibria of the curved \(N\)-body problem.
• The \(n\)-body problem in spaces of constant curvature. II: Singularities
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• Calculus and mechanics on two-point homogeneous Riemannian spaces
• The restricted two-body problem in constant curvature spaces
• Two-body problem on a sphere. Reduction, stochasticity, periodic orbits
• The restricted two-body problem and the Kepler problem in the constant curvature spaces.
• On the stability of tetrahedral relative equilibria in the positively curved 4-body problem
• Relations between integrable systems in plane and curved spaces
• Computing Planar and Spherical Choreographies
• An intrinsic approach in the curved $n$-body problem. The positive curvature case
• The Exponentially Convergent Trapezoidal Rule
• Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2
• Extension of Chebfun to Periodic Functions
• The \(N\)-vortex problem. Analytical techniques
• Libration points in spaces \(S^2\) and \(L^2\)

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