Why Does ∫δWdt = -∫δVdt?

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SUMMARY

The equation ∫δWdt = -∫δVdt is derived from the principle of Non-Ideal Interactions (NII), where force is defined as the derivative of potential energy. This relationship indicates that the work done over time is equal to the negative change in potential energy over the same interval. The discussion references a paper from the University of Oxford, which provides a detailed explanation of this concept on page 25. Understanding this equation is crucial for grasping the fundamentals of mechanics and energy conservation.

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  • Understanding of calculus, specifically integration techniques.
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  • Knowledge of Non-Ideal Interactions (NII) in mechanics.
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Gloyn
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Hi!

In this paper:

http://www.atm.ox.ac.uk/user/read/mechanics/LA-notes.pdf

On the bottom of page no. 25 there is written, that:

\int δWdt=-\int δVdt. Why is that? Can anyone explain into me?

Thanks in advance.
 
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Ok, got it, it's simply NII, force equals derivative of potential.
 

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