DYNAMICS is that division of mechanics (q.v.) which contains the doctrine of the motion of bodies produced by forces. It is essentially a science of deduction from the laws of motion (see )11oriox, LAWS oF), under which head will also be found a brief sketch of the growth of the science. The branches of D. capable of being treated in the present work will be found discussed under separate heads. We shall here confine ourselves to giving a view of the main branches and their correlation.. I. The first branch of D. deals with the fundamental conceptions of the science, their names and definitions, such as velocity (q.v.) and the different kinds of motion (q.v.), and acceler ated motion (q.v.); force, accelerating force, and moving force (see FoncE). Under this branch also falls the composition of motions (see COMPOSITION OF FORCES AND NOTIONS). II. The second main branch of D. treats of the motion, free or constrained, of points. Here two problems are solved in each case—i.e., whether the motion be free or constrained—viz., a direct and an inverse problem ; as, for example: 1. To deter mine the path of a point when the forces are given which act upon it; 2. To determine the forces or force acting on a point when its path is given. This division of dynamical problems into direct and inverse, obtains in all the branches. It may be mentioned that it was by solving the inverse problem that Newton and Huygens effected their greatest glories in connection with dynamics. The method of treating the case of a free point now generally employed, is due to Euler. See, under this head, CENTRAL FORCES; FALLING BODIES, and PROJECTILES. III. The third main branch of D. is concerned with the motion of a rigid system of points, or of a solid body. Few of the subbranches of this part of D. are capable of exposition in this work, but see CENTER
OF GYRATION, CENTER, OF OSCILLATION, CENTER OF PERCUSSION, and PENDULUM. The honor belongs to D'Alembert of establishing a general method of treating problems in rigid dynamics. Previous to his time, each set of such problems was treated on some principle peculiarly applicable to itself. D'Alembert invented one (which goes by his name) applicable to all such problems For a statement of this principle, see RIGID DYNAMICS. The fourth main branch of D. is concerned with motions of rotation. A system of rigid points may be subject to two independent kinds of motion. It may suffer a motion of translation in space, or a motion of rotation about some point or axis -within itself, or it may suffer at once a motion of translation and a rotatory motion. 'These may clearly be treated conjunctly or independently; they are now uniformly treated independently, by investigating, 1. The velocity and direction of the center of gravity of the system; and 2. The direction at each instance of the spontaneous axis of rotation passing through the center of gravity (see ROTATION), and the velocity of the rotation of the system round that axis. To effect the second task, Poinsot proposed his theory of couples (q.v.). For the conservation of living forces (virium vivarum), and the principal of least action, see FORCES. See also MOMENT. D. is used by some recent writers with a wider signification, as denoting the science which investigates the action of force (1) in compelling rest or preventing change of motion, and (2) in producing or changing motion; the former branch being called .statics, and the latter kinetics.