Conservation of Energy: Formula & Definition

AI Thread Summary
The discussion centers on the formula for the conservation of energy, emphasizing that energy cannot be created or destroyed. The key formula mentioned is dE/dt = 0, indicating that the change in energy over time is zero, which implies that the total energy remains constant. This leads to the conclusion that the energy before an event must equal the energy after, represented as Ein = Eout. Participants note the importance of considering various forms of energy, such as potential, kinetic, friction, and heat loss, when applying these principles. The conversation highlights the foundational concept that energy conservation is a fundamental principle in physics.
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What is the formula for conservation of energy?
 
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dE/dT = constant.

Or, if you prefer, the simpler

E = constant.

- Warren
 
Or: Ein = Eout
 
Oops, I meant dE/dt = 0, not constant. Of course, zero is a constant...

- Warren
 
If energy can neither be created nor destroyed - than the logical formula would be that energy before would have to equal energy after.

But you must consider potential, kinetic, friction, heat loss ect...j


Nautica
 

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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