Question

explain D'alembert's principle

Answer 1

Good Evening Student,

D’ Alembert’s principle:

The principle of virtual work states that the sum of the incremental virtual works done by all external forces $F_i$ acting in conjunction with virtual displacements δsi of the point on which the associated force is acting is zero:

 δW = Σ $F_i$ ×  δ $S_i$ = 0 ----(i)

This technique is useful for solving statics problems, with static forces of constraint. A static force of constraint is one that does no work on the system of interest, but merely holds a certain part of the system in place.

In a statics problem there are no accelerations. We can extend the principle of virtual work to dynamics problems, i.e., ones in which real motions and accelerations occur, by introducing the concept of inertial forces.

For each parcel of matter in the system with mass m, Newton’s second law states that:

F = ma ----(ii)

We can make this dynamics problem look like a statics problem by defining an inertial force

F ∗ = −ma ----(iii)

and rewriting equation (ii) as

$F_total$ = F + F ∗ = 0. ----(iv)

D’Alembert’s principle is just the principle of virtual work with the inertial forces added to the list of forces that do work:

δW = Σ $F_i$ ×  δ $S_i$ + Σ $F*_j$ ×  δ $S_j$ = 0

Let me know if you have doubts especially related to Physics, Chemistry or Maths.