On the relation between resonance and instability in planetary systems

DOI10.1007/BF01228506zbMath0518.70017OpenAlexW1984379989MaRDI QIDQ3667991

John D. Hadjidemetriou

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1007/bf01228506

zbMATH Keywords

Hamiltonian perturbationsplaneplanetary systemslinear stability behaviour of nearly circular periodic orbits

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability for problems in linear vibration theory (70J25) Celestial mechanics (70F15) (n)-body problems (70F10)

Related Items (10)

A hyperbolic twist mapping model for the study of asteroid orbits near the 3:1 resonance ⋮ Bifurcation at complex instability ⋮ Symmetric and asymmetric \(3:1\) resonant periodic orbits with an application to the 55Cnc extra-solar system ⋮ Symmetric and asymmetric librations in extrasolar planetary systems: a global view ⋮ Some instabilities in the 3/1 and 2/1 resonances ⋮ Periodic orbits of the planetary type and their stability ⋮ The elliptic restricted problem at the 3:1 resonance ⋮ Resonant motion in the restricted three-body problem ⋮ Asteroid motion near the 3:1 resonance ⋮ Periodic orbits

Cites Work

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• Families of periodic planetary-type orbits in the three-body problem and their stability
• Families of periodic orbits in the general three-body problem for the Sun-Jupiter-Saturn mass-ratio and their stability
• The restricted planetary 4-body problem
• [https://portal.mardi4nfdi.de/wiki/Publication:3868813 On the existence of periodic solutions of Poincar�'s second sort in the general problem of three bodies moving in plane]
• Periodic orbits near infinity in the restrictedN-body problem
• The continuation of periodic orbits from the restricted to the general three-body problem
• The existence of families of periodic orbits in theN-body problem

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