2007
DOI: 10.1007/s11253-007-0039-7
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Deterministic chaos of a spherical pendulum under limited excitation

Abstract: We investigate the appearance, development, and vanishing of deterministic chaos in a "spherical pendulum-electric motor of limited power" dynamical system. Chaotic attractors discovered in the system are described in detail.

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Cited by 15 publications
(2 citation statements)
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“…The excitations u(t) and v(t) will excite the pendulum directly and are simply representative of synchronous forced vibration of the system, whereas the vertical motion w(t) will excite the pendulum through principal parametric resonance if the excitation is close to an integer multiple of the linear free damped natural frequency. The most significant throughput of mechanical energy in this direction will be when that integer mul-tiple is two [5,17,26], as required for principal parametric resonance. This multiplier of two is used for the complete numerical evaluation of this work, and therefore, this work is concerned with generic forcing.…”
Section: Model Of the Spherical Pendulum With Active Power Take-offmentioning
confidence: 99%
“…The excitations u(t) and v(t) will excite the pendulum directly and are simply representative of synchronous forced vibration of the system, whereas the vertical motion w(t) will excite the pendulum through principal parametric resonance if the excitation is close to an integer multiple of the linear free damped natural frequency. The most significant throughput of mechanical energy in this direction will be when that integer mul-tiple is two [5,17,26], as required for principal parametric resonance. This multiplier of two is used for the complete numerical evaluation of this work, and therefore, this work is concerned with generic forcing.…”
Section: Model Of the Spherical Pendulum With Active Power Take-offmentioning
confidence: 99%
“…Krasnopolskaya and Shvets [7] considered the chaotic motion of deterministic parametric oscillations of a kinematically driven spherical pendulum. Later, Shvets [8] investigated the appearance, development, and vanishing of deterministic chaos in a ''spherical pendulum-electric motor of limited power'' dynamical system. He described discovered chaotic attractors.…”
Section: Introductionmentioning
confidence: 99%