Resultant (statics)

In statics the resultant of a system of forces acting at various points on a rigid body or system of particles is a single force, acting at a single point, if one exists, which is equivalent to the given system.

Suppose that forces Fi act at points ri. The resultant would be a single force G acting at a point s. The systems are equivalent if they have the same net force and the same net moment about any point.

These condition are equivalent to requiring that


 * $$G = \sum_i F_i \,$$
 * $$r \times G = \sum_i r_i \times F_i .$$