Non-Floquet oscillations of a parametrically driven rigid planar pendulum
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908990935400448 |
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| author | Sarkar, Rebeka Kumar, Krishna Khastgir, Sugata Pratik |
| author_facet | Sarkar, Rebeka Kumar, Krishna Khastgir, Sugata Pratik |
| contents | The linear and nonlinear motions of a damped rigid planar pendulum, driven by vibrating its pivot sinusoidally, are reexamined. The pendulum is known to exhibit periodic, quasiperiodic, and chaotic motions. Floquet analysis identifies regions of instability and stability within the driving parameter space. A new type of nonlinear oscillation may occur at driving parameters where Floquet analysis predicts a stable stationary state. Such non-Floquet oscillations always have periods longer than twice the period of the vibrating pivot. The possible periods of these oscillations may be four, six, eight, or twelve times the driving period. The power spectrum of the pendulum's angular velocity during these oscillations reveals a novel feature: the two dominant response frequencies sum to the driving frequency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22326 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Floquet oscillations of a parametrically driven rigid planar pendulum Sarkar, Rebeka Kumar, Krishna Khastgir, Sugata Pratik Classical Physics Chaotic Dynamics Physics Education The linear and nonlinear motions of a damped rigid planar pendulum, driven by vibrating its pivot sinusoidally, are reexamined. The pendulum is known to exhibit periodic, quasiperiodic, and chaotic motions. Floquet analysis identifies regions of instability and stability within the driving parameter space. A new type of nonlinear oscillation may occur at driving parameters where Floquet analysis predicts a stable stationary state. Such non-Floquet oscillations always have periods longer than twice the period of the vibrating pivot. The possible periods of these oscillations may be four, six, eight, or twelve times the driving period. The power spectrum of the pendulum's angular velocity during these oscillations reveals a novel feature: the two dominant response frequencies sum to the driving frequency. |
| title | Non-Floquet oscillations of a parametrically driven rigid planar pendulum |
| topic | Classical Physics Chaotic Dynamics Physics Education |
| url | https://arxiv.org/abs/2604.22326 |