Dalembert'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,

F_i + N_i + J_i = 0

where F_i is the active force applied to this point, N_i is the reaction of the constraint imposed on the point, and J_i is the inertial force, which is numerically equal to the product of mass m_i of the point and its acceleration w_i(J_i = m_iw_i 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.