The swing: Parametric resonance

Seyranian, Alexander P.

doi:10.1016/j.jappmathmech.2004.09.011

Cited by 29 publications

(15 citation statements)

References 7 publications

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“…Chaotic motions of the pendulum depending on problem parameters are investigated numerically. Here we extend our results published in [1][2][3][4] in investigating dynamics of this rather simple but interesting mechanical system.…”

Section: Pendulum With Periodically Variable Lengthsupporting

confidence: 82%

“…The dynamics of these mechanical systems is described by similar equations and is studied with the use of common methods. The material of the chapter is based on publications of the authors [1][2][3][4][5][6][7] with the renewed analytical and numerical results. The methodological peculiarity of this work is in the assumption of quasi-linearity of the systems which allows us to derive higher order approximations by the averaging method.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of a Pendulum of Variable Length and Similar Problems

Belyakov¹,

Seyranian²

2012

Nonlinearity, Bifurcation and Chaos - Theory and Applications

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Section: Pendulum With Periodically Variable Lengthsupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Dynamics of a Pendulum of Variable Length and Similar Problems

Belyakov¹,

Seyranian²

2012

Nonlinearity, Bifurcation and Chaos - Theory and Applications

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“…Let us analyze the stability of the trivial solution q = 0 of the nonlinear equation (6). Its stability with respect to the variable q is equivalent to that of Eq.…”

Section: Instability Of the Vertical Positionmentioning

confidence: 99%

“…An attempt to find the first instability region for the pendulum of variable length was undertaken in [5] but it is not correct. The stability analysis of the lower vertical position of the pendulum with damping and arbitrary periodic excitation function was carried out in [6]. In that paper the instability (parametric resonance) regions were found in the form of semi-cones in threedimensional parameter space.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the pendulum with periodically varying length

Belyakov

Seyranian

Luongo

2009

Physica D: Nonlinear Phenomena

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a b s t r a c tDynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the pendulum with periodically varying length which is also treated as a simple model of a child's swing. Asymptotic expressions for boundaries of instability domains near resonance frequencies are derived. Domains for oscillation, rotation, and oscillation-rotation motions in parameter space are found analytically and compared with a numerical study. Chaotic motions of the pendulum depending on problem parameters are investigated numerically.

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“…Change of energy and first instability region for pendulum with variable piecewise constant length were discussed by Magnus et al [5] . The stability analysis of the lower vertical position of the pendulum with damping and arbitrary periodic excitation was carried out by Seranian et al [6].The qualitative analysis of periodic solutions and their stability for PPVL no damping and orbiting excitation amplitude was studied in [7,8]. The PPVL is much less studied than the pendulum with oscillating support which is often referred to simply as a parametrically driven pendulum or parametric pendulum; These two pendula are described by different analytical models and consequently, possess different dynamical properties.…”

Section: Varying Length Pendulummentioning

confidence: 99%