# D'Alembert's principle

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## D'Alembert's principle

(dăl`əmbârz'), in mechanics, principle permitting the reduction of a problem in dynamics to one in statics. This is accomplished by introducing a fictitious force equal in magnitude to the product of the mass of the body and its acceleration, and directed opposite to the acceleration. The result is a condition of kinetic equilibrium. Jean le Rond d'Alembert, a French mathematician, introduced the principle in 1742 and established it the next year in his Traité de dynamique. The principle shows that Newton's third law of motion applies to bodies free to move as well as to stationary bodies.

## D'Alembert's principle

The principle that the resultant of the external forces F and the kinetic reaction acting on a body equals zero. The kinetic reaction is defined as the negative of the product of the mass m and the acceleration a . The principle is therefore stated as F - m a = 0. While D'Alembert's principle is merely another way of writing Newton's second law, it has the advantage of changing a problem in kinetics into a problem in statics. The techniques used in solving statics problems may then provide relatively simple solutions to some problems in dynamics; D'Alembert's principle is especially useful in problems involving constraints. See Constraint

## d'Alembert's principle

[¦dal·əm¦bərz ‚prin·sə·pəl]
(mechanics)
The principle that the resultant of the external forces and the kinetic reaction acting on a body equals zero.
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