论文标题
kapitza-whitney pendulum的平均方法
The method of averaging for the Kapitza-Whitney pendulum
论文作者
论文摘要
考虑了经典的kapitza摆的概括：在时间周期性的水平力场中，具有垂直振动枢轴点的倒平面数学摆。我们研究系统中强制振荡的存在。结果表明，始终存在一个周期性解决方案，如果振动的周期和水平力周期可以相称，则沿着摆的摆杆永远不会水平变为水平。我们还为至少存在两种不同的周期性解决方案而没有掉落的情况呈现出足够的条件。我们从数字上表明，存在稳定的周期性解决方案而不会掉落。
A generalization of the classical Kapitza pendulum is considered: an inverted planar mathematical pendulum with a vertically vibrating pivot point in a time-periodic horizontal force field. We study the existence of forced oscillations in the system. It is shown that there always exists a periodic solution along which the rod of the pendulum never becomes horizontal, i.e. the pendulum never falls, provided the period of vibration and the period of horizontal force are commensurable. We also present a sufficient condition for the existence of at least two different periodic solutions without falling. We show numerically that there exist stable periodic solutions without falling.
