Dynamics of a Rotating Sphere on Free Surface of Vibrated Granular Materials

We investigate the rotational dynamics of a low-density sphere on the free surface of a vertically vibrated granular material (VGM). The dynamical behavior of the sphere is influenced by the external energy input from an electromagnetic shaker which is proportional to \varepsilon, where \varepsilon is equal to the ratio between the square of the dimensionless acceleration \it \Gamma and the square of the vibration frequency f of the container. Empirical results reveal that as the VGM transits from local-to-global convection, an increase in \varepsilon generally corresponds to an increase in the magnitudes of the rotational \omega_\rm RS and translational v_\rm CM velocities of the sphere, an increase in the observed tilting angle \theta_\rm bed of the VGM bed, and a decrease in the time t_\rm wall it takes the sphere to roll down the tilted VGM bed and hit the container wall. During unstable convection, an increase in \varepsilon results in a sharp decrease in the sphere's peak and mean \omega_\rm RS, and a slight increase in t_\rm wall. For the range of \varepsilon values covered in this study, the sphere may execute persistent rotation, wobbling or jamming, depending on the vibration parameters and the resulting convective flow in the system.