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Derivation in classical mechanics

  1. Jun 15, 2014 #1
    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?
     

    Attached Files:

  2. jcsd
  3. Jun 15, 2014 #2

    Dale

    Staff: Mentor

    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.
     
  4. Jun 16, 2014 #3
    How? Give me examples...
     
  5. Jun 17, 2014 #4

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    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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