# 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.