Instability and periodic motion of a physical pendulum with a vibrating suspension point (theoretical and experimental approach)

Seyranian, Alexander P.; Yabuno, Hiroshi; Tsumoto, Koji

doi:10.1134/1.2074117

Cited by 16 publications

(4 citation statements)

References 4 publications

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“…In this form the instability condition was derived in Nayfeh and Mook (1979) and Thomsen (1997) Another example of stability study of a limit cycle in periodic systems was investigated both theoretically and experimentally in Seyranian, Yabuno and Tsumoto (2005). Vol.…”

Section: Stability Of Periodic Solutions In Nonlinear Systemsmentioning

confidence: 99%

Parametric Resonance in Mechanics: Classical Problems and New Results

Seyranian¹

2008

JSDD

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We formulate and solve parametric resonance problems for one-and multiple degrees of freedom systems in three-dimensional space of physical parameters: excitation frequency, amplitude, and viscous damping coefficient assuming that the last two parameters are small. The main result obtained here is that we find the instability domains (simple and combination parametric resonances) as half-cones in three-parameter space with the use of eigenfrequencies and eigenmodes of the corresponding conservative system.

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Section: Stability Of Periodic Solutions In Nonlinear Systemsmentioning

confidence: 99%

Parametric Resonance in Mechanics: Classical Problems and New Results

Seyranian¹

2008

JSDD

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“…Thus, we conclude that if the parameters satisfy strict inequality (28) there are two stable regular rotations…”

Section: Regular Rotationsmentioning

confidence: 99%

“…[9,[22][23][24][25][26][27] and references therein. Stability and dynamics of EEP have been studied analytically and numerically in [28][29][30]. Approximate oscillatory and rotational solutions for EEP are the common examples in literature [31][32][33][34] on asymptotic methods.…”

Section: Elliptically Excited Pendulummentioning

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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“…1. EEP is a natural generalization of pendulum with vertically vibrating pivot that is one of the most studied classical systems with parametric excitation, so it is often referred to simply as parametric pendulum, see for example [1][2][3][4] and references therein.…”

Section: Introductionmentioning

confidence: 99%

On rotational solutions for elliptically excited pendulum

Belyakov

2011

Physics Letters A

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The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact rotational solutions in the case of circular pivot trajectory and zero gravity. The conditions for existence and stability of such solutions are derived. Assuming that the amplitudes of excitations are not small while the pivot trajectory has small ellipticity the approximate solutions are found both for high and small linear damping. Comparison between approximate and numerical solutions is made for different values of the damping parameter.

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Instability and periodic motion of a physical pendulum with a vibrating suspension point (theoretical and experimental approach)

Cited by 16 publications

References 4 publications

Parametric Resonance in Mechanics: Classical Problems and New Results

Parametric Resonance in Mechanics: Classical Problems and New Results

Dynamics of a Pendulum of Variable Length and Similar Problems

On rotational solutions for elliptically excited pendulum

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