D’Alembert’s principle is used for

D’Alembert’s Principle

• According to the D’Alembert principle, given a system of mass of particles, the sum of the difference between the force acting on the system and the moment’s time derivatives is zero when projected onto any hypothetical displacement.
• The dynamic problem is examined using D’Alembert’s principle, which has the potential to transform it into a static equilibrium problem.
• The French mathematician and physicist Jean le Rond d’Alembert is honoured by the concept’s alternate name, the Lagrange-d’Alembert principle.
• It is a different interpretation of Newton’s Second Law of Motion.
• The second law of motion states that F = ma, although D’Alembert’s law states that F – ma = 0.
• Therefore, when a real force is exerting itself on the item, it can be considered to be in equilibrium.
• Here, F is the actual force, while ma is a made-up force that is known as the inertial force.

Summary:

D’Alembert’s principle is used for (a) reducing the problem of kinetics to equivalent statics problem (b) determining stresses in the truss (c) the stability of floating bodies (d) designing safe structures

The problem of kinetics to an equivalent statics problem can be reduced by D’Alembert’s principle. The principle states that mass of particles in a system is the sum of the difference between the force acting on the system.