The above figure illustrates the different balances a supporting body can take. These equilibria are defined as follows:

Stable Equilibrium

When a small displacement is made in the body, and this tends to return to its initial position.

Unstable Equilibrium

When a small displacement is made in the body, and this tends to move away more and more from its original position.

Indifferent Balance

When all the neighboring positions of the body are also positions of indifferent balance and, by a small displacement of the body, there are no forces that tend to return or move the body away from the initial position.

Principle of Minimum Potential Energy

An equilibrium position of a system, submitted only to conservative forces, is:

• Stable if it is at a position of minimal potential energy of the system;
• Unstable if it is at a position of maximum potential energy of the system;
• Neutral if it is at a position where there is a neighborhood in which the potential energy of the system is constant.

Stability Condition

If the body's center of gravity is in the lowest position, compared to all the others body's parts, the balance will be stable.

The equilibrium conditions of a supported body

Let's study the condition for the equilibrium of a body on a surface, where there is an application of an external force. Note that, for any object, the weight vector points to the object support base. The above figure shows a body which tends to be overturned by a force \(\vec{F}_{ext} \). In this case, while the weight vector is to the left of the normal line to the point of support, depending on the magnitude of the external force, the body will not tumble, because in this situation the weight can generate a counter torque, to compensate the torque of the \(\vec{F}_{ext}\). If the weight is on the right of the normal line, the weight will also make the body rotate and fall.