侧向扰动下单摆的轨迹分析

Analyse in Orbit of the Simple Pendulum Under the Side Direction Perturbation

采用二维谐振子模型,尝试对侧向扰动下单摆的进动现象进行分析解释,得出线性近似下摆球轨迹的极坐标公式,并对极限情况加以讨论,将单摆、圆锥摆及类椭圆摆动统一起来。进一步定性分析进动是由回复力高次项作用产生的非线性运动,从而使实验现象得到较完整的解释。

Two-dimentional simple harmonic oscillator model were used to explain the phenomenon of precession in the simple pendulum under the side direction perturbation, and deduced the polar coordinates formula of the orbit under the linear approximation, and discuss about the limit situation, put simple pendulum, cone pendulum and pseudo-ellipse pendulum united. Further qualitative analysis shown that precession is non-linear motion and produced by high-order-items of restoring force. And intact explanation of the experiment phenomenon were obtained.