On the method of introduction of local variables in a neighborhood of periodic solution of a Hamiltonian system with two degrees of freedom

DOI10.1134/s1560354723060059OpenAlexW4389429167MaRDI QIDQ6124755

Boris S. Bardin

Publication date: 2 April 2024

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

Full work available at URL: https://doi.org/10.1134/s1560354723060059

zbMATH Keywords

canonical transformationnormal formperiodic orbitKAM theoryHamiltonian systemorbital stability

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical systems in classical and celestial mechanics (37N05) Nonlinear resonances for nonlinear problems in mechanics (70K30) Normal forms for nonlinear problems in mechanics (70K45)

Cites Work

• On the orbital stability of pendulum-like oscillations and rotations of a symmetric rigid body with a fixed point
• The stability of the plane periodic motions of a symmetrical rigid body with a fixed point
• On stability of a non-autonomous Hamiltonian system in parametric resonance of dominant mode
• On the stability of a nonautonomous Hamiltonian system under second-order resonance
• On the stability of planar oscillations and rotations of a satellite in a circular orbit
• On the orbital stability of planar periodic motions of a rigid body in the Bobylev-Steklov case
• On the orbital stability of pendulum-like motions of a rigid body in the Bobylev-Steklov case
• On the Orbital Stability of Pendulum-like Oscillations of a Heavy Rigid Body with a Fixed Point in the Bobylev – Steklov Case
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
• On a Method of Introducing Local Coordinates in the Problem of the Orbital Stability of Planar Periodic Motions of a Rigid Body
• On the Orbital Stability of Pendulum Oscillations of a Dynamically Symmetric Satellite
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