Analytical methods in the theory of vibro-impact systems

DOI10.1016/0021-8928(93)90050-VzbMath0798.70008OpenAlexW2076185519MaRDI QIDQ1316665

Alexander P. Ivanov

Publication date: 10 April 1994

Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8928(93)90050-v

zbMATH Keywords

phase trajectoriesPoincaré-Bendixson theoryPoincaré mapdiscontinuitiesLyapunov's second methodLagrange-coordinate description

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Collision of rigid or pseudo-rigid bodies (70F35) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

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On the purposeful coarsening of smooth vector fields, Unnamed Item, The dynamics of systems near to grazing collision, The increasingly complex structure of the bifurcation tree of a piecewise-smooth system, Control of systems with time varying unilateral constraints using robust and optimal controllers: A homogeneity framework, Non-smooth Spatial and Temporal Substitutions in Impact Dynamics, Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability

Cites Work

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• Equations of motion of mechanical systems with ideal one-sided links
• On the generation of sets of subharmonic modes in a piecewise-continuous system
• On the behavior of dynamic systems in the vicinity of existence boundaries of periodic motions
• Doubling of the oscillation period with C-bifurcations in piecewise-continuous systems
• Bifurcations in the vicinity of a fused focus
• On the stability of periodic motions
• Stabilization Of An Impact Oscillator Near Grazing Incidence Owing To Resonance