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D'alembert's Principle

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/I'm having some doubt with D'alembert's Principle. The principle states that [itex] \sum_{i}(\vec {F}_i - \dot{\vec{p}}_i)\delta\vec{r}_i=0[/itex] but does that mean that each term of the summation must vanish too, or just the sum does? I know that mathematically there's no need that each term shall vanish, but does physical considerations requires them to vanish separately?

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