论文标题
最小驱动的Kapitza振荡器：牛顿力学和几何学的教学观点
Minimally driven Kapitza oscillator: A pedagogical perspective from Newtonian mechanics and geometry
论文作者
论文摘要
当它的枢轴点具有快速且强大的垂直振动时，简单的摆的不稳定的顶均衡点会稳定。它被称为Kapitza振荡器，在没有重力的情况下具有四个对称的平衡点，其中两个是稳定的，两个是不稳定的。 This article, completely based on a geometric argument and an elementary intuition in Newtonian mechanics, is a visual and pedagogical exposition of (a) why the oscillator has four symmetrically spaced equilibrium points in absence of gravity, (b) which of them are stable or unstable, (c) why they are so and (d) how the stability and position and number of the equilibrium points change when gravity is turned on gradually along the line of振荡器枢轴的振动。枢轴的最小冲动驱动力足以说明现象的裸露骨骼。我提出了一种在没有耗散力的情况下可以被动地维持最小动力的结构，或者如果无法消除所有耗散力，则积极积极地。在任何一种情况下，讨论的论点适用。
The unstable top-equilibrium point of a simple pendulum turns stable when its pivot point is given a fast and strong enough vertical vibration. Known as the Kapitza oscillator, it has four symmetrically spaced points of equilibrium in absence of gravity, out of which two are stable and two are unstable. This article, completely based on a geometric argument and an elementary intuition in Newtonian mechanics, is a visual and pedagogical exposition of (a) why the oscillator has four symmetrically spaced equilibrium points in absence of gravity, (b) which of them are stable or unstable, (c) why they are so and (d) how the stability and position and number of the equilibrium points change when gravity is turned on gradually along the line of vibration of the pivot of the oscillator. A minimal impulsive drive of the pivot is sufficient to illustrate the bare bones of the phenomenon. I propose a construction that can sustain the minimal drive passively in absence of dissipative forces, or actively if all dissipative forces can't be eliminated. In either of the cases, the discussed arguments apply.
