Mechanical equilibrium

denoting the static equation of motion of a system with a single degree of freedom the following calculations can be performed: When considering more than one dimension, it is possible to get different results in different directions, for example stability with respect to displacements in the x-direction but instability in the y-direction, a case known as a saddle point.

Statically indeterminate situations can often be solved by using information from outside the standard equilibrium equations.

Another example of mechanical equilibrium is a person pressing a spring to a defined point.

When the compressive force is removed the spring returns to its original state.

The minimal number of static equilibria of homogeneous, convex bodies (when resting under gravity on a horizontal surface) is of special interest.

In the planar case, the minimal number is 4, while in three dimensions one can build an object with just one stable and one unstable balance point.

An object resting on a surface and the corresponding free body diagram showing the forces acting on the object. The normal force N is equal, opposite, and collinear to the gravitational force mg so the net force and moment is zero. Consequently, the object is in a state of static mechanical equilibrium.
Diagram of a ball placed in an unstable equilibrium.
Diagram of a ball placed in a stable equilibrium.
Diagram of a ball placed in a neutral equilibrium.
Ship stability illustration explaining the stable and unstable dynamics of buoyancy (B), center of buoyancy (CB), center of gravity (CG), and weight (W)