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A theorem for planar case and its generalization for spatial case are proposed to determine the projection of a virtual displacement to the orientation under the case of knowing the projections of a virtual displacement to the given two or three orientations for object systems subject to holonomic and scleronomic constraints. Some lemmas corresponding to the two theorems for special cases are given. Applications to structural static analysis are investigated using the two theorems in this paper. Result reveals that the two theorems and corresponding lemmas are easy to be used, shorten the distance between the principle of virtual displacement and its application, and the relating problems can be solved quickly with them.

Two Theorems for Computation of Projections of Virtual Displacements and Its Application in Structural Analysis