wdoe999 said:
Gyroscopic forces play no (insignificantly small) role in keeping a bike up/stable.
As I previously mentioned, as speeds increase, gyroscopic forces resist a change in lean angle, resulting in lean stability as opposed to vertical stability. At slow to moderate speeds, the self correcting steering geometry is dominant and there is vertical stability, a bicycle and/or motorcycle have a tendency to become vertical if there is no steering input on the handlebars. At high speeds, like 100+ mph on a motorcycle (not sure what speed this would be on a bicycle), there's virtually no self-correction, and the motorcycle will just hold it's current lean angle if there's no steering input at the handlebars. Also at this speed, body leaning has virtually no effect on turning, and the counter-steering effort to change lean angle is virtuallly the same regardless if the intent is to increase or decrease lean angle.
make an unridable bike - one where the rider has no problem riding an unstable bicycle with reverse caster.
It would be very difficult to ride a bike with negative trail, it would require constant correction.
... countersteering, I should point out that in addition to turning the front wheel, another way to steer a bike is to lean to one side.
Since it's a uni-track vehicle, the center of mass remains constant, so when a rider leans to one side, the bicycle leans to the other side, which then reacts by steering to the side the bicycle is leaned, which ultimately is just an indirect method of implementing counter-steering. As mentioned above, at very high speeds on a motorcycle, leaning doesn't work, only direct counter steering.
This works fine for a single wheel, but two conical wheels, one in front of the other, and with parallel axis will roll in a straight line (slippage occurs instead of turning). I'll try to find a website that ran this experiement and update this post later.
update -
http://www.terrycolon.com/1features/bike1.html
Let's say you turn the bike's wheel to the left .. low speeds
Then the bike will lean right, even at low speeds. Since there's little resistance to counter-steering at low speeds it's not as noticable.
staying upright on a bicycle with no forward or backward movement
This is possible because the trail causes the contact patch to move sideways relative to the rest of the bicycle, so a very skilled rider (like a velodrome racer) can generate corrective torque forces with steering inputs, similar to counter-steering, but the range of movment is very small. Trials riders will sometimes use a free leg to generate corrective torque force balance a trials motorcyle, in addition to hopping the bike around like a pogo stick with two contact patches.
The dynamics of two wheeled vehicles can confuse the issue of counter steering, because of body leaning, gyroscopic effects, ... This is why I find the most accurate information regarding counter-steering is found in web sites that explain the dynamics of unicycles