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MTW Exercise 6.9

  1. Oct 9, 2014 #1

    TerryW

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    Can anyone help with the attached problem. A simple yes or no answer only is required, but if you want to point me in a particular direction......
     

    Attached Files:

  2. jcsd
  3. Oct 9, 2014 #2

    Mark44

    Staff: Mentor

    The three equations in the attachment represent a coupled system of three differential equations. There are not three variables - there are six, the three variables and the three derivatives of these variables.

    Since the question is more about solving a system of differential equations, and less about relativity, I am moving the thread to the technical math section.
     
    Last edited: Oct 9, 2014
  4. Oct 9, 2014 #3

    TerryW

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    I think you have answered my question. Thanks
     
    Last edited by a moderator: Oct 9, 2014
  5. Oct 9, 2014 #4

    dextercioby

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    You have both t and tau. Did you mean to write only 1 variable?
     
  6. Oct 9, 2014 #5

    Mark44

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    I noticed that as well. My guess is that it should be one of them, not both.
     
  7. Oct 10, 2014 #6

    TerryW

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    The equations are correct and do include both t and tau, but this works out OK because dt/d(tau) = gamma

    Don't bother to spend any more time on this - the message is clear that I have six variables and only three equations so I have to 'take a guess' at what the solutions may be.


    TerryW
     
  8. Oct 10, 2014 #7

    Mark44

    Staff: Mentor

  9. Oct 14, 2014 #8
    I looked at this problem, and I suggest turning the S's into these combinations: S0, (S1*cos(ω*t)+S2*sin(ω*t)), (-S1*sin(ω*t)+S2*cos(ω*t)), or reversed signs for sin(ω*t) if necessary. You will find three differential equations for them. Since the coefficients are constant, you can easily make them vary as exp(λ*τ), where you must find λ.
     
  10. Oct 24, 2014 #9

    HallsofIvy

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    You switched symbols in the middle of the equations. Are we to assume that "S1" is the same as "S1", etc.?
     
  11. Oct 24, 2014 #10

    TerryW

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    In this case, S1 = η11S1.

    As I said in my reply to Dextercioby and Mark44, the answer telling me that I have 6 variable was all I needed, so please don't worry about this any further on my behalf.


    Regards


    TerryW
     
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