Three-dimensional periodic orbits about the triangular equilibrium points of the restricted problem of three bodies

DOI10.1007/BF01230339zbMath0591.70010OpenAlexW2038881078MaRDI QIDQ3719883

C. G. Zagouras

Publication date: 1985

Published in: Celestial Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01230339

zbMATH Keywords

family of periodic orbitscollinear equilibrium pointfourth-order termstriangular equilibrium pointsfamily of nonsymmetric three-dimensional periodic orbitsthird-order parametric expansionsthree-dimensional periodic solutionstriangular point

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Three-body problems (70F07) Stability for nonlinear problems in mechanics (70K20) Dynamical systems and ergodic theory (37-XX)

Related Items (12)

Vertical bifurcation families from the long and short period families around the equilateral equilibrium points ⋮ On bridges \(B(pL, qS)\) around triangular libration points ⋮ The small-energy three-body systems ⋮ Unchained polygons and the \(N\) -body problem ⋮ Vertical stability of periodic solutions around the triangular equilibrium points ⋮ Three-dimensional bifurcations of periodic solutions around the triangular equilibrium points of the restricted three-body problem ⋮ Computation of Periodic Solutions of Conservative Systems with Application to the 3-Body Problem ⋮ Bifurcation points and intersections of families of periodic orbits in the three-dimensional restricted three-body problem ⋮ Motion close to the Hopf bifurcation of the vertical family of periodic orbits of \(L_{4}\) ⋮ A database of planar axisymmetric periodic orbits for the solar system ⋮ Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem ⋮ High-order solutions around triangular libration points in the elliptic restricted three-body problem and applications to low energy transfers

Cites Work

• Three-dimensional periodic oscillations generating from plane periodic ones around the collinear Lagrangian points
• The three-dimensional motion of Trojan asteroids
• The Trojan Manifold in the System Earth-Moon
• Out-of-plane motion about libration points: Nonlinearity and eccentricity effects

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