When I took control theory at university, in the last lecture, the lecturer took out a bike with rear wheel steering and challenged us to ride it in the hallway outside the lecture hall in the break. No one could get it to roll more than a couple of meters. The second half of the lecture was spent proving that a rear wheel steered bike is in fact (almost) impossible to control.

And in opposite world: Rockets with steering thrusters near their top are highly unstable.

At some point (some) people though rockets with the thrusters near the top would be more stable. See e.g. this rocket by Robert H. Goddard: https://en.wikipedia.org/wiki/Robert_H._Goddard#/media/File:...

But it turns out that it doesn't matter whether you place the thrusters high or low, stability-wise. What matters is that the center of mass is in front of the center of the center of pressure.

Aren't they just as stable as regular rockets, but it's very inconvenient to put the thrusters on top? It's called pendulum rocket fallacy and from what I can tell that's the case.

Huh, wouldn't this be similar to riding a regular bike backwards, which a lot of people (although not myself) are able to do?

Yes, it was pretty much a reverse bike with the saddle on the frame and a handle bar just behind where the seat post should be, connected to the steering axle. The details is a little bit fuzzy since it was a couple of years ago but iirc it is actually possible bike backwards at slow speeds but require a lot more active balancing from the rider, and at some point it becomes impossible as the speed increases. Also it concerned the case where the bike is riding straight ahead, it is possible that it is easier to control if riding in a curve.

In the extreme, it's also equivalent to a unicycle - just lean back to put all your weight on the steering back tire. Unicycles can be controlled.

Both are undeniably less easy than a normal bicycle though.

> opposite direction turning

The term used in motorcycling is countersteering. A lot of people think they are using their body to change direction but that would not be sufficient. Also it helps to be deliberate about the handlebar pushing motion for safety and performance.

I also recommend the SmarterEveryDay video[0] where they rig a bike to turn the opposite way than it is steered.

[0] https://www.youtube.com/watch?v=MFzDaBzBlL0

A fair bit of the stability of a bicycle (especially at low speeds) is due to the fact that you have a human holding onto a bar that behaves exactly like a thing that a human would grab onto to steady themselves. If you grab this bar and rotate it clockwise, then you yourself will rotate anticlockwise - and that is true whether the bar is the handlebars on a bike or a random bar fixed on a wall. Holding ourselves steady by grabbing onto something is something that humans have a remarkably effective and quick feedback loop for, which is why bicycle riding comes naturally once you get over the fear of falling off and just do what feels right.

Rigging the handlebars to turn the wheel the other way cancels out that automatic feedback loop.