KAM dynamics and stabilization of a particle sliding over a periodically driven curve

DOI10.1016/j.aml.2006.05.023zbMath1130.70320OpenAlexW2089553908MaRDI QIDQ878990

Pedro J. Torres, Daniel E. Nuñez

Publication date: 4 May 2007

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2006.05.023

zbMATH Keywords

Lyapunov stabilitytwist conditionKAM dynamics

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (4)

Quantifying Poincaré's continuation method for nonlinear oscillators ⋮ Twist periodic solutions in the relativistic driven harmonic oscillator ⋮ Lyapunov stability of elliptic periodic solutions of nonlinear damped equations ⋮ On the motion of an oscillator with a periodically time-varying mass

Cites Work

• The inverted pendulum: A singularity theory approach
• The stability of the equilibrium of a pendulum for vertical oscillations of the point of suspension
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• The stability of the equilibrium of a conservative system
• Stability of the Inverted Pendulum—A Topological Explanation
• The Stability of the Equilibrium of a Nonlinear Hill’s Equation
• A Lyapunov-type stability criterion using $L^\alpha $ norms
• Stabilization of the Inverted Linearized Pendulum by High Frequency Vibrations
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