From Goldstein:

A virtual (infinitesimal) displacement of a system refers to a change in the configuration of the system as the result of any arbitrary infinitesimal change of the coordinates $$\delta\mathbf{r}_i$$, consistent with the forces and constraints imposed on the system at the given instant $$t$$.

From my Mechanics instructor (not verbatim):

A virtual displacement is a displacement consistent with the system's constraints.

My instructor's definition of virtual displacement is crystal clear and Goldstein's isn't so I can't determine if they're compatible. What does Goldstein mean by "consistent with the forces"? I find this phrase to be extremely ambiguous. After clearing that up, please discuss the equivalence or lack thereof of these two statements.

• Well it looks like your instructor's definition of contained within the book's definition. – Aaron Stevens Mar 3 '19 at 22:27
• More on virtual displacement. – Qmechanic Mar 4 '19 at 7:09