Can one move a van, caravan or trailer with a push from within?

No, you cannot push or pull it a distance from the inside.

That results because when you use a force there is always a counter force. [Newt's Third Law of Motion] You push with your hands and body weight, and the counter force, to keep you from sliding away is the friction force at your feet. And as both the force and counter force are acting on the same body, the van, they offset each other and the net force, which is what would make things move, is zero.

In math talk, f = P - F = 0 = MA [Newt's Second Law] where P is the push or pull and F = P is the counter force. So the van with mass M does not accelerate (A = 0) and due to its inertia [Newt's First Law] stays put.

As some other answers allude to, there are other ways, other than a push or pull, that can make the van move when applied from the inside.

For example, you can take a running leap at one of the front or back walls while the van is in neutral. And when you smack into it, you will impart an impact force F = dP/dT where dP is your change in momentum upon impact. And in this case, the offsetting force is the force that would accelerate the van away from your direction.

But don't expect much of a move as the mass of the van M >>> m your mass; so from the conservation of momentum Mv = mU and v = (m/M)U is the expected initial speed for the van when you with mass m smack into the wall with speed U >> v.

A rowboat analogy is easier to visualize.

If you weigh 50 kg, and you are standing in a 50kg

rowboat one meter from the dock;

as you walk one meter from stern to stem in the

rowboat, the rowboat will move one meter further

from the dock leaving you the same distance

from the pier.

You can sometimes move it an inch or two from inside, but it is likely to roll back to the original location. There is a slight possibility of starting it to roll down a long hill. Wedges under each tire, are a good precaution.

Yes, by sudden displacement of the weight inside.

Just read "The Martian"

This is a passage which directly links to your question.

“ I’ve got to bring that down.

But how?

I’ll roll the damn airlock.

It’s basically a phone booth on its side. I did some experiments.

I figured if I want it to roll, I’ll need to hit the wall as hard as possible. And I have to be in the air at the time. I can’t press against some other part of the airlock. The forces would cancel each other out and it wouldn’t move at all.

First I tried launching myself off one wall and slamming into the other. The airlock slid a little, but that’s it.

Next, I tried doing a super-push-up to get airborne (0.4 g yay!) then kicking the wall with both feet. Again, it just slid.

The third time, I got it right. The trick was to plant both my feet on the ground, near the wall, then launch myself to the top of the opposite wall and hit with my back. When I tried that just now, it gave me enough force and leverage to tip the airlock and roll it one face toward the Hab.

The airlock is a meter wide, so…sigh…