I started studying Lagrangian mechanics, so I want to completely understand the concept of virtual displacement "in all types of constrained systems" in order to understand virtual work and d' Alembert principle to derive Lagrange Equations of motion.
Virtual displacement is a fictitious displacement field imposed on a structure, with the constraints of boundary conditions and continuity requirements. Generally, the actual forces are allowed to do virtual work by moving with the virtual displacement. Virtual displacement can also be viewed as a variation in the sense of calculus of variations when a strain energy functional exists.
Virtual displacements are displacements (think also as fictitious or virtual displacements, that is not associated to a specific force system) that satisfy perfect constraint conditions (i.e., homogeneous constraint relationships) and associated to fixed (not time depending) constraints.
I read in reference such as; Greenwood and Schaum outline of lagrangian mechanics that virtual displacements do not necessary obey the constraints, and you say they do, as other reference such as; Hand,finch and Greiner. How can I deal with this conflict?
PS: I haven't studied the calculus of variations yet.
Constraints are generally grouped into displacement constraints and force constraints.The virtual displacements have to meet the displacement constraints.
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