参数驱动刚性平面单摆的非Floquet振荡
Non-Floquet oscillations of a parametrically driven rigid planar pendulum
AI总结：
研究参数驱动刚性平面单摆的线性和非线性运动，发现非Floquet振荡具有比振动支点周期长的周期，且功率谱显示响应频率之和等于驱动频率。
摘要：
对一个受振动支点驱动的阻尼刚性平面单摆的线性和非线性运动进行了重新审视。该单摆已知会表现出周期性、拟周期性和混沌运动。Floquet分析确定了驱动参数空间内的稳定和不稳定区域。在Floquet分析预测稳定静止状态的驱动参数下，可能产生一种新的非线性振荡。此类非Floquet振荡的周期始终长于两倍的振动支点周期。这些振荡的可能周期可能是四、六、八或十二倍的驱动周期。在这些振荡期间，单摆角速度的功率谱揭示了一个新特征：两个主导响应频率之和等于驱动频率。
英文摘要：
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.
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