The Composition and Resolution of Force Systems

Any number of forces are always reducible to a single force and a single couple whose plane is perpendicular to the direction of the force. So that there is always in space a certain determinate straight line . . . which may serve at the same time to represent the line of action of the resultant, and the axis of the resultant couple . . . this central axis . . . gives us so luminous a reduction of all of the forces of the system as to throw a light at the same time upon all the other equivalent reductions, and to group them, so to speak, into a single picture, in which we see at once order and mutual dependence.
—L. Poinsot, Éléments de Statique (1803).

Mechanics is the science of motion and has as its object the investigation of the position and configurations of systems of material bodies as a function of time. The aim of this investigation is to arrive at the simplest description of the facts which are observed in nature and, from this description, to form generalizations which will permit valid predictions as to the behavior of other systems.

The motions that occur in nature are the result of interactions between the various bodies which make up the system under consideration. That portion of the subject of mechanics which describes the motion of bodies, without reference to the causes of the motion, is called kinematics. That portion of the subject which studies the relationship between the mutual influences and the resulting motions is called kinetics. The subjects of kinematics and kinetics are often considered together under the name of dynamics. That portion of the subject which studies the conditions under which the interactions between bodies counteract each other, with a resultant state of rest or of uniform motion, is called statics. When the mutual influences between the bodies of a system counteract each other so that the system is either at rest or moves with a uniform velocity, the system is said to be in equilibrium. Statics, then, is the study of the conditions of equilibrium. In a large number of engineering problems the structures or mechanisms which are under consideration are in equilibrium, so that the subject of statics assumes an important place in the field of applied mechanics.