Some classical mechanics

While it'll take a while to get all my Paris pictures sorted out, I've fallen back to some light internet reading. Forget your quarks, photons, neutrinos and whatever else in physics that are way beyond my comprehension. Have you ever stopped to think about how a bicycle works? Have you actually cared enough to find out afterwards? Well, today's the day I answer yes. My first thought was that gyroscopic forces from the spinning wheels keep the bicycle stable and upright. As it turns out, people have gone to great lengths to disprove that theory. Behold the zero-gyro bike, where two counter-rotating wheels cancel the gyroscopic effect of the main wheels. As it turns out, while it is very possible to ride a zero-gyro bike, it is impossible to ride a bike with its steering column locked in the forward position, unless the wheels are huge and gyroscopic forces actually dominate. Thus, it's actually the act of the rider that keeps a bike upright. As the figure shows, the bike is balanced as long as the moments created by gravity and centrifugal force balance each other. The system itself is not stable without a feedback controller, the rider. The rider has control over v, r and q by the acts of peddling, steering and leaning, which offers enough redundancy to ensure the moments are balanced even with external disturbances. Evidently, the bike cannot be balanced when v is zero because a centrifugal force is not possible, not because there is no gyroscopic effect from rotating wheels. On the other hand, here's a monstrocity I've only discovered today: the gyro monorail. While it might intuitively work like a bicycle, it's actually quite different. There is no control over r (due to the fixed tracks), and it would be difficult to control q directly. Thus this thing stays up purely by a giant spinning gyroscope inside the cabin. A control system keeps control over the precession of the gyroscope, which maintains the balance of the vehicle. At first glance it seems strange to see this thing stand, but after reading the article, I'm actually convinced that this system has a lot of advantages over traditional two rail systems. As the co-inventor Piotr Schilovski pointed out, it was generally ignorance in the engineering community that prevented this idea from being implemented.