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Mechanics questions

  1. Sep 24, 2014 #1
    1. The problem statement, all variables and given/known data

    The difference between the Euler and Lagrange equations and when to use each.
    How to set up Lagrange when the energies are non-holonomic such as friction.
    What is the difference between curly delta and plain derivative, eg Hamilton's equation

    2. Relevant equations
    Euler's equation vs. Lagrange equation and Hamilton's equation


    3. The attempt at a solution
    These are general conceptual questions. Please see the attached sheet for more detail. I just need a little more understanding rather than help on a specific problem. Links to sites giving more detailed explanations would be greatly appreciated.
     

    Attached Files:

  2. jcsd
  3. Sep 26, 2014 #2
    1) The equation is called the Euler-Lagrange equation - your question doesn't make much sense, unless you're referring to Euler's Equations in the context of rotating reference frames.

    2) Non-holonomic constraints are a very advanced subject actually, and generally you can't deal with them. With friction, you have to come up with some model, but often [itex] \vec{F} = -|\dot{\vec{r}}|^{\alpha}\hat{r}[/itex] is a good approximation.

    3) The total derivative of a function is defined in terms of partial derivatives. Example:

    [itex] \frac{df(x,y,z,t)}{dt} = \frac{\partial f(x,y,z,t)}{\partial x}\frac{\partial x}{\partial t} + \frac{\partial f(x,y,z,t)}{\partial y}\frac{\partial y}{\partial t} + \frac{\partial f(x,y,z,t)}{\partial z}\frac{\partial z}{\partial t} + \frac{\partial f(x,y,z,t)}{\partial t} [/itex]
     
  4. Sep 30, 2014 #3
    Thanks for your response. It turned out I was so confused that I did not state the questions correctly. Please see attachment for answers which will clear up the confused questions.
     

    Attached Files:

  5. Oct 1, 2014 #4

    BvU

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    I can comment on the last question: What it says there is that q(t) is the function that minimizes the action integral.
    So you are not looking for a variable value that minimizes something, for which you use a differential (usually indicated with a ##d##), but for a path from t1 to t2 for wich you use this variational notation ##\delta##
     
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