DYNAMICS OF A BEAD ON A ROTATING RING

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.