Consider what happens in front wheel steering, such as an automobile:
- Turn the steering wheel slightly clockwise.
- The front wheels each turn slightly clockwise.
- Their rolling action causes the wheels to pull the front end of the vehicle slightly to the right.
- The back wheels follow the track of the front wheels, but in a slightly tighter turn.
- Holding the steering wheel in that position will cause the vehicle to continuously turn in a circle.
- The wheels' caster makes them try to return to a neutral position.
The wheels are mounted with "caster", meaning that the almost vertical axis about which the wheels rotate when steered doesn't meet the ground at the same position as where the wheels meet the ground.
This causes sideways friction when the wheels are not in a straight-forward position (negative feedback).
This is a very stable arrangement:
- Turns are circular.
- The sharper the desired turn, the more the steering wheel must be turned.
- Releasing control causes the steering to automatically return to a neutral position.
Now consider what happens in rear wheel steering, such as a fork-lift (or when driving a car in reverse):
- Turn the steering wheel slightly clockwise.
- The back wheels each turn slightly counter-clockwise.
- Their rolling action causes the wheels to push the back end of the vehicle slightly to the left.
- The front wheels continue forward, turning to the right, but in a slightly tighter turn.
- Holding the steering wheel in that position will cause the back wheels to steer more and more widely around the front wheels, which make an increasingly tighter turn.
- Depending on the caster, the wheels might have a tendency to steer even more when released.
This is a very unstable arrangement:
- To drive a circular path, the driver must initiate the turn by swinging the back end out to the left, and then must continuously reduce the amount of steering to avoid following a spiral path.
- Releasing control does not return the steering to neutral, and will likely result in a very tight spiral.
Rear wheel steering is very handy at slow speed.
A fork-lift for example can position the front end, push it into place, and adjust the back end to line up square.
Similarly, it is easier to back a car into a parking spot than to drive in forward, and much easier to drive out forward.
But at higher speed, rear wheel steering is inherently unsafe. With front wheel steering, if something goes wrong, the vehicle ends up going straight. With rear wheel steering, if something goes wrong, the vehicle ends up spiraling out of control.
Edit: a simpler explanation:
The OP commented: "Shopping carts have no caster, but they do have trail. But I don't see how trail can be responsible, seeing as the same swiveling casters are stable if in front, but unstable if in the back. There must be another explanation.", and yes, there is another explanation. I mentioned negative feedback, but failed to expand on the idea.
Imagine what happens when a vehicle turns to the right.
As a passenger, you feel yourself pulled to the left by a force (some physicists say a virtual force) known as centrifugal force.
This same force acts on the vehicle itself, though because it is a rigid object you don't notice it except perhaps for a slight tip to the left.
Now consider how the vehicle's wheels react to this force, looking at three different types of vehicles:
On a railroad car, the wheels are not steerable and are attached to a fixed axle. This means that both wheels must roll at the same rate, even though when going around a curve one wheel has to travel a greater distance. Centrifugal force behaves as if it acts on the car's center of gravity and pushes all the wheels to the left.
The track, and the surface of the wheels themselves are not, as one might think, perfectly level. Instead they slope to the inside so that the part of the wheel that hangs over the inside of the rail has a larger diameter than the part of the wheel that hangs over the outside of the rail.
When the car turns, and is pushed to the left, the left wheels end up rolling on their larger diameter section while the right wheels run on their smaller diameter section. In effect, the car has larger wheels on the left and smaller wheels on the right, and it naturally turns to the right, following the track. (At slow speed this effect doesn't happen, hence the loud squealing of slipping wheels in shunting yards.)
On a vehicle with front-wheel steering, the centrifugal force also acts on the center of gravity and pushes all the wheels to the left. The rear wheels are fixed and so continue following the vehicle. The front wheels can turn, so as they push to the left against the ground, the ground pushes them to the right. With caster, or trail, this force provides negative feedback that makes the wheels return to their normal straight-forward position unless a steering wheel is forcing them to stay in a turned position.
On a vehicle with rear-wheel steering, it is the front wheels that are relatively unaffected by the sideways force, and the rear wheels that react to it. The force of the road on the wheels makes them want to turn to the left. But the vehicle is turning because the rear wheels were already turned to the left, so in this case the centrifugal force provides positive feedback. The more the vehicle turns, the more the wheels tend to make it turn. Rather than forcing the vehicle to turn, the steering wheel must be used to prevent the vehicle from turning.
The rail car is symmetric front to back, asymmetric side to side, and steers by a very different mechanism using both front and rear wheels.
The front-steering vehicle's front wheels are affected by negative feedback, which forces the steering back to a neutral position.
The rear-steering vehicle's rear wheels are affected by positive feedback, which forces the steering into ever increasing turn positions.
Negative feedback is generally a good thing, enforcing stability (e.g. thermostats).
Positive feedback is generally a bad thing, causing rapid unrestricted growth (e.g. explosions, PA system howling).
Historical side notes:
Since they don't use rolling wheels, ships and planes steer from the rear because in that situation, rear steering is more stable.
It's no longer done this way, but the traditional ship steering wheel used to be turned the opposite way to how it is turned in a car. (Notice in the description above how steering clockwise caused the rear wheels to turn counter-clockwise. Having the steering wheel turn the same way as the rudder made sense.)
One would move the top of the steering wheel to the left in order to turn the ship to the right.
Planes on the other hand do still use this "backward" steering.
When steering, the pilot pushes on the right rudder pedal in order to yaw to the right.
This is the exact opposite of how anyone that has used a soap-box car with single axle front steering would expect it to work.
Bureaucrats and social idealists are often ignorant of the laws of physics, which tend to conflict with their world-view.
In the 1970s Joan Claybrook, as head of the US National Highway Transportation and Safety Administration, somehow discovered that motorcycles were more dangerous to their drivers than were cars.
As a result, she commissioned, at great expense to the taxpayers, the design of a "safe" motorcycle.
Naturally it had a steel-pipe roll-cage to protect the driver.
And since her friend Ralph Nader had already killed the Chevrolet Corvair because he incorrectly believed that rear-engine vehicles were "unsafe at any speed", she had the motorcycle's engine mounted at the front.
This of course meant that the steering had to go at the back.
Anyone that has ever walked along, pushing a bicycle without holding the handlebars, knows that it's easy to go forward and impossible to go backward.
The engineers and other professionals working on the project pointed out that her design wouldn't work, but she dismissed negative "opinions" of the naysayers, her ideals of highway safety taking precedence over reality.
Eventually it was given a pair of outrigger wheels (effectively the same as training wheels on a child's first bicycle), because no one was able to drive it without it almost immediately tipping over.
Here's an image of the prototype (the driver would sit facing the right):