# Can all systems be put in equilibrium?

I'm in a first year statics course. We have spent the whole semester solving for forces and moments so that the system is in equilibrium.

When we are given a system, we immediately begin solving for all variables for the system to be in equilibrium. But how do we know that the system can be put in equilibrium? I asked my prof about this and he said that all systems can be solved to be put in equilibrium, but some systems might possibly have multiple solutions.

Why can all systems be put in equilibrium? If I misunderstood the prof and all systems can't be put in equilibrium, is there a quick way to check if a system can be put in equilibrium? (Other than the obvious way of solving the system).

Thanks.

• Comment to the question (v1): The idealized model of a free-falling particle $L=\frac{1}{2}m\dot{q}^2-mg q$ does not have an equilibrium. Commented Oct 19, 2013 at 19:55

Your teacher is right, but only in the context of the course he's teaching you. By definition, statics deals with systems in equilibrium or that can reach equilibrium. In other cases, like thermodynamics, you can have systems that can only approach equilibrium asymptotically -- that is, they can be very close to equilibrium but never quite reach it.

• Could you give me a definition of a "static system"? In other words what properties must a system have to be able to be put in equilibrium?
– dfg
Commented Oct 19, 2013 at 20:00
• The actual definition of a static system is one that only depends on the state of its components at a given time $t$, whereas a dynamic system depends on the history of its components, that is, on its evolution for $-\infty<t<0$, being $t=0$ its present state. Commented Oct 19, 2013 at 20:05
• Could you give me a proof that all static systems can be put into equilibrium?
– dfg
Commented Oct 19, 2013 at 20:09
• A static system is deterministic and therefore, if there is no interaction from the outside, it will have to eventually reach some kind of equilibrium state. The only other possibility would be to have a chaotic behaviour but those sytems are not static. Commented Oct 19, 2013 at 20:32
• But why can't a static system have some unbalanced force that causes it to keep accelerating? Why does it have to come to an equilibrium?
– dfg
Commented Oct 19, 2013 at 20:36