First-order resonances in three-degrees-of-freedom systems

DOI10.1007/BF01686817zbMath0547.70018OpenAlexW2035762532MaRDI QIDQ3339350

Els van der Aa

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1007/bf01686817

zbMATH Keywords

periodic orbitsHamiltonian systemsasymptotic integrabilityresonance-ratio

Mathematics Subject Classification ID

Hamilton's equations (70H05) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06)

Related Items

Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems ⋮ Singular reduction of resonant Hamiltonians ⋮ Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance ⋮ On the integrability of Hamiltonian 1:2:2 resonance ⋮ Hamiltonian Hopf bifurcations near a chaotic Hamiltonian resonance ⋮ On the integrability of twofold 1 : 2 Hamiltonian resonance ⋮ Non-integrability of first order resonances in Hamiltonian systems in three degrees of freedom ⋮ The \(1 : 2 : 4\) resonance in a particle chain ⋮ On detuned 1:1:3 Hamiltonian resonance with cases of symmetric cubic and quartic potentials ⋮ On the detuned 2:4 resonance ⋮ The coupled 1:2 resonance in a symmetric case and parametric amplification model ⋮ All relative equilibria of Hamiltonian in detuned 1:2:3 resonance ⋮ An asymptotic analysis of the 1:3:4 Hamiltonian normal form ⋮ Periodic orbits ⋮ Integrability and non-integrability of Hamiltonian normal forms

Cites Work

• Lyapunov's center theorem for resonant equilibrium
• Normal modes for nonlinear Hamiltonian systems
• Asymptotic Integrability and Periodic Solutions of a Hamiltonian System in $1:2:2$-Resonance
• Disappearance of integrals in systems of more than two degrees of freedom
• Birkhoff's normalization