Dalembert's Principle

D’alembert’s Principle


one of the primary principles of dynamics according to which a system of forces in equilibrium is obtained if the inertial forces are combined with the given (active) forces acting on the points of a mechanical system and with the reactions of imposed constraints. It is named after the French scientist J. d’AIembert. From d’Alembert’s principle it follows that, for any ith point of a system,

Fi + Ni + Ji = 0

where Fi is the active force applied to this point, Ni is the reaction of the constraint imposed on the point, and Ji is the inertial force, which is numerically equal to the product of mass mi of the point and its acceleration wi(Ji = miwi and directed opposite to this acceleration. D’Alembert’s principle makes it possible to apply the simpler methods of statics to solving problems of dynamics, and therefore it is widely used in engineering practice. It is especially convenient to use for determining reactions of the constraints in cases where the law of the motion taking place is known or has been found from solving the corresponding equations.