旋转圆环上的珠子动力学

DYNAMICS OF A BEAD ON A ROTATING RING

对于放置在旋转圆环凹槽上的珠子,当圆环旋转时,珠子将产生一系列运动行为。可以将珠子视为刚体,研究珠子的动力学,考虑滚动摩擦和黏滞阻力两种形式的阻力,用分析力学方法推导其运动方程,并讨论相关动力学变量,包括平衡点超临界分叉、小振动周期等条件,通过实验模型进行逐一验证。并对特殊条件下进行的受迫振动进行了理论和实验研究。

For a bead placed on a rotating ring,when the ring rotates,the beads will produce a series of motion behaviors.The bead can be considered as a rigid body.Two forms of resistance,rolling friction and viscous resistance,are considered,and their equations of motion are derived by analytical mechanics.Relevant kinetic variables are discussed,including supercritical pitchfork bifurcation at the equilibrium point,small vibration period,which are verified one by one through the experimental model.The forced vibration under special conditions is studied theoretically and experimentally.