In most of classical mechanics textbooks,the concept of virtual displacement and virtual work is not represented deeply.They just focus in how the method should be used with out explaining from where this principle came and why scientists created it in the first place. So to grasp this concept do I need to have a solid background in differential geometry and topology? I'm saying this because I read in Wikipedia that:" virtual displacement arises from differentiating with respect to the parameter ε enumerating paths of the motion varied in a manner consistent with the constraints (thus pointing at a fixed time in the direction tangent to the constraining manifold)". The manifold is a topological concept and it is related also to differential geometry. In fact I'm trying to grasp Lagrangian mechanics,and I think that virtual displacement and work are like a cornerstone to enter deeply in the subject. Thanks in advance!!