Capture into resonance and escape from it in a forced nonlinear pendulum

DOI10.1134/S1560354713060087zbMath1286.70024arXiv1309.6501OpenAlexW3106512175MaRDI QIDQ2449295

Anatoly I. Neishtadt, Aleksey A. Vasiliev, Anton V. Artemyev

Publication date: 7 May 2014

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

Full work available at URL: https://arxiv.org/abs/1309.6501

zbMATH Keywords

pendulumadiabatic invariantautoresonancecapture into resonance

Mathematics Subject Classification ID

Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics (70H11) Multiple scale methods for ordinary differential equations (34E13) Nonlinear resonances for nonlinear problems in mechanics (70K30) Averaging of perturbations for nonlinear problems in mechanics (70K65)

Related Items (10)

Direct and inverse secondary resonance effects in the spherical motion of an asymmetric rigid body with moving masses ⋮ Capture and keeping of a resonance near equilibrium ⋮ Separatrix maps in slow-fast Hamiltonian systems ⋮ Capture into parametric autoresonance in the presence of noise ⋮ Local adiabatic invariants near a homoclinic set of a slow-fast Hamiltonian system ⋮ Capture and holding of resonance far from equilibrium ⋮ Parametric stability of a charged pendulum with an oscillating suspension point ⋮ Jumps of energy near a homoclinic set of a slowly time dependent Hamiltonian system ⋮ Crossing of the critical energy level in Hamiltonian systems with slow dependence on time ⋮ Autoresonance in oscillating systems with combined excitation and weak dissipation

Cites Work

• Unnamed Item
• Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave
• A second fundamental model for resonance

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