1999
DOI: 10.1016/s0021-8928(99)00028-3
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The dynamics of a spherical pendulum with a vibrating suspension

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Cited by 23 publications
(19 citation statements)
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“…The dynamics and control of a pendulum with a vibrating point of suspension have been investigated extensively [1][2][3][4]. The first application of a spherical pendulum to capture the complex dynamics of a payload motion of a boom crane was reviewed by Abdel-Rahman et al [5].…”
Section: Introductionmentioning
confidence: 99%
“…The dynamics and control of a pendulum with a vibrating point of suspension have been investigated extensively [1][2][3][4]. The first application of a spherical pendulum to capture the complex dynamics of a payload motion of a boom crane was reviewed by Abdel-Rahman et al [5].…”
Section: Introductionmentioning
confidence: 99%
“…While swinging, to maintain the oscillations one can crouch half as often. Despite the popularity of the swing, in the literature on oscillations and stability [1][2][3][4][5][6][7][8][9][10][11][12][13][14], where this problem is referred to, there are no general formulae for describing the regions of instability, which explain the phenomenon of the swinging of a swing. The problem of the instability of a swing is solved below using an approach which involves the use of the derivatives of the monodromy matrix with respect to the parameters [15][16][17][18].…”
mentioning
confidence: 99%
“…Similarly, if the spherical motion of the payload is assumed (Ghigliazza and Holmes, 2002;Markeyev, 1998), with h = h 0 , _ h ¼ € h ¼ 0 and uj t=0 = u 0 , the equation governing the motion of the spherical pendulum of the payload is obtained as…”
Section: A Special Case With Rigid Structure Assumptionmentioning
confidence: 99%