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sams

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In Chapter 7: Hamilton's Principle, in the Classical Dynamics of Particles and Systems book by Thornton and Marion, Fifth Edition, page 258-259, we have the following equations:

1. Upon squaring Equation (7.117), why did the authors in the first term of Equation (7.118) are summing over two indices ##j## and ##k##, and not over ##j## only? In other words, where did the index ##k## come from? Why do we add sometimes a new index and when do we do that?

2. What is the physical interpretation of Equation (7.121)?

Thanks a lot!

1. Upon squaring Equation (7.117), why did the authors in the first term of Equation (7.118) are summing over two indices ##j## and ##k##, and not over ##j## only? In other words, where did the index ##k## come from? Why do we add sometimes a new index and when do we do that?

2. What is the physical interpretation of Equation (7.121)?

Thanks a lot!