d’Alembert’s principle, alternative form of Newton’s second law ofmotion, stated by the 18th-century French polymath Jean le Rond d’Alembert. In effect, the principle reduces a problem in dynamics to a problem instatics. The second law states that theforceFacting on a body is equal to the productof the massmandaccelerationaof thebody, orF=ma;in d’Alembert’s form, the forceFplus the negative of the massmtimes accelerationaof the body is equal to zero:F-ma= 0. In other words, the body is inequilibriumunder the action of the real forceFand the fictitious force -ma. The fictitious force is also called aninertial forceand a reversed effective force.Because unknown forces are more easily determined on bodies in equilibrium than on moving bodies, theforce andstressanalysis of machine components can usually be simplified by using inertial forces. When developing the formulas for the stresses in a rotating disk, for example, it is convenient to assume that a representative element in the disk is in equilibrium under the action of a system of radial and tangential forces produced by the stresses and an outward-acting inertial (centrifugal) force.
Posted on: Sat, 08 Mar 2014 04:37:27 +0000
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