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We report the unexpected precessional motion when a small,rigid ring is rotated on a vertical smooth rod. Using high speed imaging, two distinct regimes of motion were observed experimentally. (1)Oscillatory motion when the ring has 1 contact with the rod (transient motion).(2) Steady state (terminal velocity)when the ring has2 instantaneously stationary contacts with the rod. These two regimes and the transition between them are analyzed through qualitative, analytical and numerical means. One key feature of the steady-state motion is energy dissipation through rolling friction and air drag, which were modeled theoretically with coefficients independently characterized. Our model predicted that steady-state motion occurs only when certain geometric conditions(ratio of radii of ring and rod,tilt angle)are fulfilled. Our numerical simulations accounts for the stick-slip transition at the contact point.As the steady state regime was often found to be the preferred final state, dynamic stability of single-contact was investigated through bifurcation,phase space and linear stability analyses.Theoretical models are in good agreement with experimental data across all experiments.Our findings have potential applications in various engineering fields,such as studying the vibrational detachment of threaded fasteners and developing gravity-driven centrifuges. 發(fā)自小木蟲Android客戶端 |
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