Virtual work and constraint forces

[Ahmed1029]

Suppose I'm considering a system of N particles that are constrained in their possible motions and so there are less that 3N generalized coordinates. Suppose now I perform a virtual displacement on one particle, which due to some constraints might force some other particles to more virtually with it, like the case of an atwood machine. I now want to calculate the virtual work done by the constraint forces on the particles that move as a corrolary to the movement of this single particle plus the work done on this particle itself, can I get a non-zero result? I'm asking because the book I'm reading assers that the virtual work done by virtually moving ALL the particles has to be zero, and not necessarily the work done to move a single particle has to be zero.

 

[andresB]

The principle of virtual works asserts that the net/total virtual work is 0.

https://arxiv.org/pdf/physics/0011004.pdf