On the motions of one near-autonomous Hamiltonian system at a 1:1:1 resonance

DOI10.1134/S1560354719030018zbMath1428.70037OpenAlexW2948996744MaRDI QIDQ2284593

Olga V. Kholostova

Publication date: 15 January 2020

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354719030018

zbMATH Keywords

stabilityperiodic motionHamiltonian systemresonanceconditionally periodic motioncylindrical precession of a satellite

Mathematics Subject Classification ID

Orbital mechanics (70M20) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12) Nearly integrable Hamiltonian systems, KAM theory (70H08) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (3)

On Nonlinear Oscillations of a Time-Periodic Hamiltonian System at a 2:1:1 Resonance ⋮ On Nonlinear Oscillations of a Near-Autonomous Hamiltonian System in the Case of Two Identical Integer or Half-Integer Frequencies ⋮ On Nonlinear Oscillations and Stability of Coupled Pendulums in the Case of a Multiple Resonance

Cites Work

• Nonlinear oscillations of a 1:1 resonance Hamiltonian system
• On nonlinear motions of Hamiltonian system in case of fourth order resonance
• Loss of stability in Hamiltonian systems that depend on parameters
• Versal normal form of the Hamiltonian function of the restricted problem of three bodies near \({\mathcal L}_ 4\)
• On motions near the Lagrange equilibrium point \(L_4\) in the case of Routh's critical mass ratio
• A study of the motions of an autonomous Hamiltonian system at a 1:1 resonance
• A unifying theory in determining periodic families for Hamiltonian systems at resonance
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• Convergent series expansions for quasi-periodic motions
• An extension to resonant cases of Liapunov's theorem concerning the periodic solutions near a Hamiltonian equilibrium
• On the applicability of the third integral of motion
• Periodic solutions for dynamical systems possessing a first integral in the resonance case
• Lyapunov's center theorem for resonant equilibrium
• The interaction of resonances of the third and fourth orders in a Hamiltonian two-degree-of-freedom system
• Nonsemisimple 1?1 resonance at an equilibrium
• Periodic solutions near a resonant equilibrium of a Hamiltonian system
• On periodic motions of a nonautonomous Hamiltonian system in one case of multiple parametric resonance
• On the periodic motions of a Hamiltonian system in the neighborhood of unstable equilibrium in the presence of a double three-order resonance
• Formal stability of Hamiltonian systems
• Periodic orbits emanating from a resonant equilibrium
• Periodic orbits near ?4 for mass ratios near the critical mass ratio of routh
• Pseudo-oscillator with a quartic perturbation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the motions of one near-autonomous Hamiltonian system at a 1:1:1 resonance