Studies of Melnikov method and transversal homoclinic orbits in the circular planar restricted three-body problem

DOI10.1007/BF02498706zbMath0954.70012MaRDI QIDQ1367436

Cheng Xiang, Ruzeng Zhu

Publication date: 11 February 2001

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

zbMATH Keywords

Poincaré sectionenergy surfaceextended Melnikov methodMcGehee transformationcircular planar restricted three-body problemdegenerate fixed point small mass ratioglobal phase diagramnear-integrable Hamiltonian systemtangle phenomenontransversal homoclinic and heteroclinic orbits

Mathematics Subject Classification ID

Three-body problems (70F07) Dynamical systems in classical and celestial mechanics (37N05) Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics (70K44) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (4)

A note on the existence of a Smale horseshoe in the planar circular restricted three-body problem ⋮ Unnamed Item ⋮ Study on Chaotic Behavior of the Restricted Four-Body Problem with an Equilateral Triangle Configuration ⋮ The existence of transversal homoclinic orbits in a planar circular restricted four-body problem

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Global bifurcations and chaos. Analytical methods
• A stable manifold theorem for degenerate fixed points with applications to celestial mechanics
• Determination of the potential in a synodic system
• Unnamed Item
• Unnamed Item

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