On the Logical Status of the Virtual Work Law

The law of virtual work (VWL) is probably the first law in the history of mechanics; it is previous to the one on the lever, though not completely distinct from it. Here I will discuss the logical status of VWL, that is whether it is an autonomous principle or a theorem of some sort of mechanics. The problem is complicated by the fact that up to now no universally recognised expression has been accepted for it. From this article the problematical nature of VWL demonstrability is quite clear when the mechanics does not characterise completely the constraints. Italian schools in the XVIII century, even if we do not take Lagrange into consideration, had an important role, both in the development of VWL and in the discussion of its role.