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I am going through a PDF by Subhankar Ray & J. Shamanna on virtual work here and according to the PDF, equation 29, they write gerneralized force as:

  1. $$Q_j = -\nabla_k\tilde{V}\cdot\left(\frac{\partial\textbf{r}_k}{\partial q_j}\right) = -\frac{\partial V}{\partial q_j}\tag{29}$$

But shouldn't it be:

  1. $$Q_j = -\sum^N_{k=1}\nabla_k\tilde{V}\cdot\left(\frac{\partial\textbf{r}_k}{\partial q_j}\right) = -\frac{\partial V}{\partial q_j}~?$$

And according to Goldstein, page 22, just above eq(1.54), they also don't drop the summation.

Why did they drop the summation in (1)?

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1 Answer 1

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It is either a typo or that eq. (29) uses Einstein summation convention.

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