Here's what I originally typed out before googling:
The "something about the geometry" is called caster, and is the same effect that makes the front casters on a shopping cart go straight: the point where the steering axis intersects the ground is ahead of the contact patch of the tire. On a bike, this is mostly determined by the angle of your head tube when looking at the bike from the side (if the fork is "bent" from the side view, this would also contribute to the caster effect).
But I've now googled, and found a paper that says that a bike can be stable without gyroscopic or caster effects [1]. It seems like the specific mass distribution of the steerable mass (front wheel, fork, handlebars, etc) vs the rest of the frame matters, and of course all of these variables interact in complex ways. They do agree that caster plays an important role though.
Vehicle dynamics is notoriously tricky stuff. I can say with experience that it doesn't get easier when you go to four wheels.
The "something about the geometry" is called caster, and is the same effect that makes the front casters on a shopping cart go straight: the point where the steering axis intersects the ground is ahead of the contact patch of the tire. On a bike, this is mostly determined by the angle of your head tube when looking at the bike from the side (if the fork is "bent" from the side view, this would also contribute to the caster effect).
But I've now googled, and found a paper that says that a bike can be stable without gyroscopic or caster effects [1]. It seems like the specific mass distribution of the steerable mass (front wheel, fork, handlebars, etc) vs the rest of the frame matters, and of course all of these variables interact in complex ways. They do agree that caster plays an important role though.
Vehicle dynamics is notoriously tricky stuff. I can say with experience that it doesn't get easier when you go to four wheels.
[1]: https://www.researchgate.net/publication/51051995_A_Bicycle_...