# What type of displacement is virtual displacement? Is it really a displacement? How to calculate it? [duplicate]

Searched this question a lot in different places but could not find any answer that could satisfy me. So I am here to clear my concepts regarding virtual displacement. Now I am clarifying my doubt.

As my textbook "A Student’s Guide to Lagrangians and Hamiltonians" by Hamill says on p.11:

A virtual displacement, $$δx_i$$, is defined as an infinitesimal, instantaneous displacement of the coordinate $$x_i$$, consistent with any constraints acting on the system.

And it gives the relationship, $$\delta x_i=\sum_{\alpha=1}^n\frac {\delta x_i}{\delta q_\alpha}$$ The time co-ordinate is frozen in virtual displacement. Now my question is if time is frozen then no displacement should occur. So how the "Virtual displacement" come? What does it mean?

Again $$\frac {\delta x_i}{\delta q_\alpha}$$ how is it getting the dimension of a displacement? I think the $$x$$'s and $$q$$'s dimension is same [L]. So it should be dimensionless.

Please illustrate it so that I do not face any difficulties with virtula-displacement term. I will be too much helpful if you also give an example to show how to calculate virtual displacement.

• Does this answer your question? What exactly is a virtual displacement in classical mechanics? Commented Jul 30, 2020 at 15:45
• No I could not understand from this. It is not clearing my concept. Commented Jul 30, 2020 at 15:49
• Possible duplicates: physics.stackexchange.com/q/456771/2451 , physics.stackexchange.com/q/520835/2451 , physics.stackexchange.com/q/289522/2451 and links therein. Commented Jul 30, 2020 at 19:46
• @Qmechanic Sir I am an undergraduate student and all we read are very introductory level. All those possible questions you suggest are not of my level of understanding. So if you can answer plz answer in a easiest manner. And I have also asked something which was not asked in any of those questions. [dimensions, how to calculate (physical example),]. Please help me in clearing my concept Commented Jul 31, 2020 at 4:52