Intuition suggests if you want to stabilize something, you remove energy; but for some systems, the removal of energy has an unexpected effect: destabilization. Take, for instance, a top—a toy designed to spin rapidly on a flat surface. When it’s inert, it lays off to its side, but when it is spinning, the motion allows it to stay balanced on its tip. As time goes on, the top meets with the friction of the table beneath it and the air molecules surrounding it. As energy leaves the system, it becomes unstable—its motions are now unpredictable and uneven, until finally, the top comes to a rest.
The reason for this counter-intuitive behavior of such spinning objects was first proved on physical grounds by Lord Kelvin and Tait in 1867 and disseminated in their famous Treatise on Natural Philosophy. About a century later, it was proved mathematically by the Russian mathematical physicist Chataev. It has become an important long-accepted paradigm in the theory of stability. It says that a gyroscopically stabilized system—one that gains stability through a spinning motion, like a top or a spacecraft—becomes unstable when there is dissipative damping—removal of energy. In recent research published in the AIAA Journal, Firdaus Udwadia, professor of aerospace and mechanical engineering, civil and environmental engineering, and information and operations management at the USC Viterbi School of Engineering, learned that such systems can actually become exponentially stable if dissipative damping is accompanied by an infusion of energy. Done just the right way, the cooperative interaction of the injection and removal of energy can significantly elevate the system’s stability, creating a whole new paradigm in stability theory.
Said Udwadia: “What it says is the paradigm of stability has to be altered or changed. Kelvin and Tait never thought of injecting and simultaneously removing energy to stabilize a system, because the injection of energy to do this is counter-intuitive. The prevailing paradigm has been in use for 150 years. This discovery provides the opportunity to make many such mechanical and aerospace systems extremely stable, something that was thought impossible to do in the presence of dissipative damping.”