The Equilibrium of Force Systems

Prop. 6: Commensurable magnitudes balance at distances reciprocally proportional to their weights. Prop. 7: And now, if the magnitudes be incommensurable, they will likewise balance at distances reciprocally proportional to the magnitudes. — Archimedes (287-212 в.c.), On Plane Equilibrium.

In the preceding chapter the problem of reducing any type of force system to the simplest possible equivalent force system has been solved. In many practical problems the forces acting upon a system are balanced so that the resultant force is equal to zero. In the present chapter the conditions under which this equilibrium condition is obtained will be investigated. We shall first establish the equations of equilibrium for the general three-dimensional force system.