to spontaneously develop an instability, i.e. without some external force acting on it?
A stable system remains stable even when an external force does act on it. That is the definition of stability. Systems can be conditionally stable, e.g. stable in one state but not in another.
Do you mean like if you lock me up in a box sitting on the floor, is it possible for me, inside the box, to tip the box over?
In general it is always possible to add enough energy to a system to destabilize it. Stability refers to a system that returns to its original state after a small input of energy.
A box on the floor is stable, if you tip it a bit it will rock back in place. It is possible to add enough energy to tip the box completely over or even break the box.
I'm pretty sure the point of the OP's question is to ask if this can happen without introducing energy from an external source.
I agree that it sounds to be, by definition, impossible.
What about the example in post#3 of me inside the box?
you cant create energy, so no it cant be
Who said anything about creating energy? Is there anything that says the closed system cannot contain stored energy, like say, a bored Web Developer with a point to make?
Hello? Is this thing on?
If you manage to tip the box over, its only because of the force of the floor, which is an external force.
To imagine a closed system, imagine trying to tip the box over in intergalactic space (impossible).
If it is possible to tip the box over, then it isn't stable.
I think this is a matter of definition: a stable system is by definition something that doesn't develop spontaneously an instability.
I would say that a person in a box is a conditionally stable system. The condition being that the person keeps themselves within certain bounds (below a certain height and velocity etc.) within the box. If the person exceeds those bounds then the box can spontaneously tip over, but if the person does not exceed those bounds then small external inputs will not result in the box tipping over.
Not at all. If I turn myself in a circle inside the box, it will rotate in the opposite direction. True, its CoM will not have moved, but its orientation has.
You sure about that definition?
The way the question in the OP is worded, it is basically the same as asking if it is possible for 1 to equal 2. We don't need to nitpick the definition when the OP used two words with opposite meanings and asked if they can be equal.
Exactly, I'd just like to word it differently. The system of the person is conditionally stable, the condition being if the net external force on the system is zero. When you push the box sideways, you're inducing gravitational force that would otherwise be canceled out by the normal force. Now if the system were isolated, that's a completely different story.
Separate names with a comma.