Symmetric trajectories for the \(2N\)-body problem with equal masses
From MaRDI portal
Publication:880933
DOI10.1007/s00205-006-0030-8zbMath1111.70010OpenAlexW2095450204MaRDI QIDQ880933
Andrea Venturelli, Susanna Terracini
Publication date: 21 May 2007
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00205-006-0030-8
Related Items (41)
Variational aspects of the two-center problem ⋮ Periodic solutions of the planar \(N\)-center problem with topological constraints ⋮ Hip-hop solutions of the \(2N\)-body problem ⋮ On the variational approach to the periodic \(n\)-body problem ⋮ The Lagrange reduction of the \(n\)-body problem, a survey ⋮ Hill’s formula for $g$-periodic trajectories of Lagrangian systems ⋮ A symmetric spatial periodic orbit in the \(2n\)-body problem ⋮ Geometric properties of minimizers in the planar three-body problem with two equal masses ⋮ Periodic Oscillations in a \(2{N}\) -Body Problem ⋮ Periodic oscillations in the restricted hip-hop \(2N+1\)-body problem ⋮ Symmetric constellations of satellites moving around a central body of large mass ⋮ Entire minimal parabolic trajectories: the planar anisotropic Kepler problem ⋮ Platonic polyhedra, topological constraints and periodic solutions of the classical \(N\)-body problem ⋮ New periodic solutions for some planar \(N + 3\)-body problems with Newtonian potentials ⋮ Braids with the symmetries of Platonic polyhedra in the Coulomb (N+1)-body problem ⋮ New periodic solutions for planar \((N+2)\)-body problems ⋮ Avoiding collisions under topological constraints in variational problems coming from celestial mechanics ⋮ Unchained polygons and the \(N\) -body problem ⋮ Morse index properties of colliding solutions to the \(N\)-body problem ⋮ Platonic polyhedra, periodic orbits and chaotic motions in the \(N\)-body problem with non-Newtonian forces ⋮ Torus knot choreographies in the n-body problem ⋮ Syzygy sequences of the -center problem ⋮ Scattering parabolic solutions for the spatial \(N\)-centre problem ⋮ Topologically distinct collision-free periodic solutions for the \({N}\)-center problem ⋮ A continuum of periodic solutions to the planar four-body problem with two pairs of equal masses ⋮ A minimizing property of hyperbolic Keplerian orbits ⋮ Highly eccentric hip-hop solutions of the \(2N\)-body problem ⋮ Removing collision singularities from action minimizers for the \(N\)-body problem with free boundaries ⋮ On the minimizing triple collision orbits in the planar Newtonian three-body problem ⋮ On the stability of periodic N-body motions with the symmetry of Platonic polyhedra ⋮ Symmetries and choreographies in families that bifurcate from the polygonal relative equilibrium of the \(n\)-body problem ⋮ Spatial double choreographies of the Newtonian \(2n\)-body problem ⋮ From the Lagrange polygon to the figure eight. I: Numerical evidence extending a conjecture of Marchal ⋮ New periodic solutions for Newtonian \(n\)-body problems with dihedral group symmetry and topological constraints ⋮ Periodic solutions to a forced Kepler problem in the plane ⋮ On the minimality of Keplerian arcs with fixed negative energy ⋮ The Broucke–Hénon orbit and the Schubart orbit in the planar three-body problem with two equal masses ⋮ Globally minimizing parabolic motions in the Newtonian \(N\)-body problem ⋮ A study of the apsidal angle and a proof of monotonicity in the logarithmic potential case ⋮ The monotonicity of the apsidal angle in power-law potential systems ⋮ Star pentagon and many stable choreographic solutions of the Newtonian 4-body problem
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The principle of symmetric criticality
- Periodic solutions for N-body type problems
- Symmetry groups and non-planar collisionless action-minimizing solutions of the three-body problem in three-dimensional space
- Symmetry groups of the planar three-body problem and action-minimizing trajectories
- Central configurations of the N-body problem via equivariant Morse theory
- Collisionless periodic solutions to some three-body problems
- Total collison, completely parabolic motions and homothety reduction in the \(n\)-body problem
- Non-collision periodic solutions of the N-body system
- The \(n\)-body problem and mutual distances
- Binary decompositions for planar \(N\)-body problems and symmetric periodic solutions
- On central configurations
- How the method of minimization of action avoids singularities
- On the existence of collisionless equivariant minimizers for the classical \(n\)-body problem
- Simple Choreographic Motions of N Bodies: A Preliminary Study
- Symmetries and noncollision closed orbits for planar N-body-type problems
- Multiplicity of eigenvalues for the Laplace operator with respect to an obstacle, and nontangency conditions
- A Minimizing Property of Keplerian Orbits
- Minima de l'intégrale d'action et équilibres relatifs de n corps
- Variational methods on periodic and quasi-periodic solutions for the N-body problem
- Action minimizing orbits in then-body problem with simple choreography constraint
- Minima of the action integral in the Newtonian problem of 4 bodies with equal masses: `Hip-hop' orbits
- A remarkable periodic solution of the three-body problem in the case of equal masses
- Action-minimizing orbits in the parallelogram four-body problem with equal masses
This page was built for publication: Symmetric trajectories for the \(2N\)-body problem with equal masses
