A family of symmetrical Schubart-like interplay orbits and their stability in the one-dimensional four-body problem

DOI10.1007/s10569-005-2289-8zbMath1145.70007OpenAlexW2048159551MaRDI QIDQ817662

Winston L. Sweatman

Publication date: 17 March 2006

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-005-2289-8

zbMATH Keywords

periodic orbitsfour-body problemcollinear motioninterplay motions

Mathematics Subject Classification ID

Celestial mechanics (70F15) (n)-body problems (70F10) Collisions in celestial mechanics, regularization (70F16)

Related Items (15)

Analytical stability in the Caledonian symmetric five-body problem ⋮ Symmetric Four-Body Problems ⋮ Periodic solutions with alternating singularities in the collinear four-body problem ⋮ Existence and stability of symmetric periodic simultaneous binary collision orbits in the planar pairwise symmetric four-body problem ⋮ Families of double symmetric ``Schubart-like periodic orbits ⋮ Linear stability analysis of symmetric periodic simultaneous binary collision orbits in the planar pairwise symmetric four-body problem ⋮ Ejection-collision orbits in the symmetric collinear four-body problem ⋮ Linear stability for some symmetric periodic simultaneous binary collision orbits in the four-body problem ⋮ Stability of the rhomboidal symmetric-mass orbit ⋮ Existence and linear stability of the rhomboidal periodic orbit in the planar equal mass four-body problem ⋮ Existence of the Broucke periodic orbit and its linear stability ⋮ A global regularisation for integrating the Caledonian symmetric four-body problem ⋮ The family of planar periodic orbits generated by the equal-mass four-body Schubart interplay orbit ⋮ Stability of Broucke's isosceles orbit ⋮ Some qualitative features of the isosceles trapezoidal four-body problem

Cites Work

• A numerical investigation of the one-dimensional Newtonian three-body problem. II: Positive energies
• A numerical investigation of the one-dimensional Newtonian three-body problem
• Regularization of simultaneous binary collisions in the \(n\)-body problem
• Triple collision in the collinear three-body problem
• An implementation of \(N\)-body chain regularization
• A slow-down treatment for close binaries
• The symmetrical one-dimensional Newtonian four-body problem: A numerical investigation
• Numerische Aufsuchung periodischer Lösungen im Dreikörperproblem
• Stability of interplay motions
• Chaos in the one-dimensional gravitational three-body problem
• The Caledonian symmetrical double binary four-body problem. I: Surfaces of zero-velocity using the energy integral

This page was built for publication: A family of symmetrical Schubart-like interplay orbits and their stability in the one-dimensional four-body problem