傅科摆的进动与轨迹的周期性

Rotation of the oscillation plane of Foucault pendulum and periodicity of trajectory

利用守恒量求解傅科摆小摆角相对运动方程,解析解是内次摆线.确定了轨迹的曲率半径和周期轨迹的形成条件.证明了摆球速度矢量是以匀角速度-ωsinλ旋转的.

The relative motion equation of Foucault pendulum is solved by using the conservation law and its exact solution is a hypotrochoid in the polar coordinate. Both curvature radius and periodic formation of trajectory are determined by means of the geometric property of hypotrochoid. It is proved that the rotation speed of vector of velocity is always equal to -ωsin λ.