principle of d'Alembert for the material point



If we consider a system that consists of a number of material points, highlighting a certain point with a known mass under the action attached to her external and internal forces she gets some acceleration relative to the inertial systemreference.Among such forces may be as active forces and the reaction link.

Inertia point - a vector quantity, which is equal in absolute value to the mass point on its acceleration.This value is sometimes referred to as dalamberovskuyu force of inertia, it is directed opposite to acceleration.In this case reveals the following property of a moving point: in each moment of inertia for added strength to the point of actually existing forces, the resulting force system is balanced.So it is possible to formulate the principle
of d'Alembert for one material point.This statement is fully consistent with Newton's second law.

Principles d'Alembert system



If repeat all the arguments for each point in the system, they lead to the following conclusion, which expresses the principle of D'Alembert formulated for the system: if at any point in time to make the inertia force to each of the points in the system,Besides the actual acting external and internal forces, then the system will be in equilibrium, therefore it is possible to apply all the equations that are used in static.

If we apply the principle of d'Alembert to solve the problems of dynamics, the equations of motion of the system can be formed in the shape that we know the equilibrium equations.This principle simplifies calculations and makes the approach to solving one.

Applying the principle of D'Alembert



Note that a moving point in a mechanical system are only the external and internal forces that arise as a result of the interaction points between themselves and also with the bodies outside the given system.Points move with acceleration detection under the influence of these forces.Inertial forces are not acting on the moving point, otherwise, they would be moved without acceleration or were alone.

forces of inertia are introduced only to create dynamic equations using a simple and convenient method of statics.Also taken into account that the geometric sum of the internal forces and the sum of the moments is zero.Using the equations that are derived from the principle of D'Alembert, it makes the process of solving problems easier, because these equations do not contain the internal forces.