So what exactly is the difference between these two things? I understand their individual uses perfectly well, I think (or perhaps hope), but I'm a little unclear on what exactly a virtual displacement is. is it just a sort of imagined displacement that can't really occur, while a differential displacement is just an infinitesimally small but still physically significant displacement? Further, is there any sort of mathematical basis behind virtual displacement? Of course infinitesimal quantities can he defined using limits or hyperreal numbers; is there any analagous sort of construction for virtual quantites, or is it more of a physics-based idea? I'm sorry if I'm being unclear, it's possible I just don't know exactly what sort of question to ask.