Applied Mathematics seminar | Prof. Dong Eui Chang, On the Damping-Induced Self-Recovery Phenomenon in Mechanical Systems

The falling cat problem has been very popular in control, mechanics and mathematics since Kane and Sher published a paper on this topic in 1969. A cat, after released upside down, executes a 180-degree reorientation, all the while having a zero angular momentum. It makes use of the conservation of angular momentum that is induced by rotational symmetry in the dynamics. In general, however, the angular momentum is not conserved if there is a symmetry-breaking force, such as a frictional force, on the system.

 

Recently, we have discovered an exciting phenomenon in controlled mechanical systems with external damping forces. If a control force is activated on such a system for a while and then gets deactivated, the unactuated cyclic variables, which get excited initially from rest by the control force, eventually all converge back to their initial values as time tends to infinity, which is called a damping-induced self-recovery phenomenon.

 

A self-recovery phenomenon can be observed in the simple experiment with a rotating stool and a bicycle wheel which is a typical setup in physics classes to demonstrate the conservation of angular momentum. Sitting on the stool, one spins the wheel by hand while holding it horizontally. A reaction torque will be created to initiate a rotational motion of the stool in the opposite direction. After some time, if the person applies a braking force halting the wheel spin, then the stool will asymptotically return to its original position, as if it has a memory, provided that there is a viscous damping force on the rotation axis of the stool.

 

We have also discovered the self-recovery phenomenon in incompressible viscous fluid flows. As a corollary, we give a "dynamic" explanation of the famous experiment by G.I. Taylor on the "kinematic" reversibility of low-Reynolds-number flows.

 

In this talk, several videos will be displayed to show instances of damping-induced self-recovery phenomena.