# Virtual displacement and D'Alembert's principle

## Main Question or Discussion Point

While deriving lagrangian equation using D'Alembert's principle, in Goldstien, they defined a variable called "virtual displacement". Why do we need a concept called virtual displacement? What is its signigicance in classical physics?

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Hi,

http://en.wikipedia.org/wiki/Virtual_displacement

I am not an expert on this matter but from what I have seen, virtual displacements are small spatial displacements $r_{i}$ (with no time displacement) over the path of motion and are used in Lagrangian mechanics.

The least action principle is part of Lagrangian mechanics and states that particles follow a path whose action is stationary, which means that any "small" virtual displacements does not change the action.