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.

  • $\begingroup$ Well it looks like your instructor's definition of contained within the book's definition. $\endgroup$ Mar 3, 2019 at 22:27
  • $\begingroup$ More on virtual displacement. $\endgroup$
    – Qmechanic
    Mar 4, 2019 at 7:09

1 Answer 1


Goldstein made a mistake. This is a screenshot from the errata.

Error in Goldstein


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