Derivation in classical mechanics

  • Thread starter Jhenrique
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  • #1
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I'm studying classical mechanics and I'm stumbling in the quantity of differential identities.

Being S the action, H the hamiltonian, L the lagrangian, T the kinetic energy and V the potential energy, following the relationships:

attachment.php?attachmentid=70623&stc=1&d=1402838216.png


But, the big question is: that's all? Or has exist more?

Seems be missing
$$\frac{\partial S}{\partial q'} \;\;\; \frac{\partial S}{\partial p} \;\;\; \frac{\partial S}{\partial p'} \;\;\; \frac{\partial S}{\partial q'} \;\;\; \frac{\partial L}{\partial p} \;\;\; \frac{\partial L}{\partial p'} \;\;\; \frac{\partial H}{\partial p'} \;\;\; \frac{\partial H}{\partial q'} \;\;\; \frac{\partial V}{\partial q'} \;\;\; \frac{\partial V}{\partial p} \;\;\; \frac{\partial V}{\partial p'} \;\;\; \frac{\partial T}{\partial q} \;\;\; \frac{\partial T}{\partial p} \;\;\; \frac{\partial T}{\partial p'}$$
These relation exist? Make sense? If yes, how will be the identities?
 

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Answers and Replies

  • #2
Dale
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Once you write down the Hamiltonian or the Lagrangian then you certainly can write down all of the rest of those quantities, but there is no point it doing so. You can already solve the equations of motion without them.
 
  • #3
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Once you write down the Hamiltonian or the Lagrangian then you certainly can write down all of the rest of those quantities

How? Give me examples...
 
  • #4
Vanadium 50
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First, it's please give me examples. We are not your servants, to be ordered around.

Second, you're essentially asking us to write down a textbook for you. I'm afraid that's beyond what one can reasonably expect PF to do. You are going to have to do some work on your own.

This looks like a good time to close this thread.
 

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