Dynamic modeling and nonlinear oscillations of a rotating pendulum with a spinning tip mass

In this work, a dynamic model of a rotating pendulum with a spinning tip mass is developed. The pendulum is rotating with a prescribed angular velocity around the vertical axis, while the tip mass spins around an arbitrary axis with constant angular velocity. The dynamic stability and bifurcation of the system are examined first for the pendulum when rotating with a constant angular velocity. The effects of the tip mass spin on the dynamic equilibrium and stability are thoroughly examined by constructing the bifurcation diagrams and phase plane portrait plots. It is found the tip mass spin considerably affects the qualitative nonlinear behavior and stability of the system. The frequency response of the pendulum due to sinusoidal angular rotation of the pendulum around the vertical axis is obtained using numerical integration combined with an arc-length continuation scheme. The effects of the magnitudes and directions of the tip mass spin on the nonlinear dynamic behavior of the system are subsequently investigated.