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 F_i act at points r_i. 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

$G=\sum _{i}F_{i}\,$

$r\times G=\sum _{i}r_{i}\times F_{i}.$