Equation of Virtual Work VS Potential Energy

AI Thread Summary
The virtual work equation for linear elastic materials resembles the potential energy equation, differing primarily by a (1/2) coefficient in the internal work term of the potential energy equation. This discrepancy arises from the distinct methods of load application in virtual work compared to potential energy calculations. The discussion seeks clarification on the origin of the (1/2) coefficient in the potential energy equation. Participants express confusion regarding the explanation of this coefficient. Understanding the relationship between load application and energy calculations is essential for grasping these concepts.
rdbateman
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For linear elastic materials (3D General)...

The virtual work equation looks exactly like the equation for potential energy except that in the potential energy equation, the internal work term has a (1/2) coefficient. Why are these different?
 
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Do you know why the potential energy has a 1/2 coefficient?

It has to do with the method of application of the loads, which is different for VW.
 
That doesn't answer the question.
 
Actually I did provide an answer, albeit very short.

But I still don't know if you understand where the 1/2 comes from.
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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