Lagrange-d’Alembert Principle

Lagrange-d’Alembert principle is generally known as D’Alembert’s principle, stated by French physicist and mathematician polymath Jean le Rond d’Alembert.

According to the d’Alembert’s principle, the external forces acting on a body and the resultant inertia forces on a body are in equilibrium. This principle is a alternative form of Newton’s Second law of motion but this principle suggests that the term “-ma” (product of mass and acceleration) of the body can be considered as a fictitious force, often called the inertia force or d’Alembert’s force. Accordingly, the net external force F actually acting on the body and the inertia force Fi together keep the body in a state of fictitious equilibrium.

F + Fi = 0

The d’Alembert’s principle gives the solution procedure of a dynamic problem, an appearance like that of a static problem and the above equation becomes equation of dynamic equilibrium.

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