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Goldstein said:Note that there is no dependence of time, [tex]\delta t[/tex] is involved here( in the definition of virtual displacement that is [tex]\delta \vec{r_{i}}=\sum_{j} \frac{d \vec{r_{j}} \delta q_{j}}{d q_{j}}[/tex] ) ,since a virtual displacement by def depends only on the displacement of coordinates.(Only then is the virtual displacement perpendicular to the force of constraint if the constarint itself is changing with time.)

Can someone Prove the thing in bold letters?