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Notation for Velocity Gradient

  1. Jul 6, 2012 #1
    This is not a problem statement this is not homework this is not a textbook exercise. This is my own question about a formula in a textbook.

    1. The problem statement, all variables and given/known data

    I am trying to understand the way that equation 4.2.2 is rewritten as equation 4.2.3

    2. Relevant equations

    8VDbY.jpg
    Source: Stanley Middleman

    3. The attempt at a solution

    My confusion is with the 1/2 and the subscripts used.
     
  2. jcsd
  3. Jul 6, 2012 #2

    cepheid

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    4.2.2. is NOT rewritten as 4.2.3. On the contrary, 4.2.3. is just an expression for the velocity gradient, a new thing that has been just introduced in the preceding description.

    As for the factors of 1/2: just *expand* the stuff in parentheses on the right-hand side out, and you'll see that it is equal to the stuff on the left-hand side.

    What, specifically, about the subscripts is confusing you? Basically both indices i and j can take on any of the values [1,2,3]. So you can think of 4.2.3 as a compact way of writing a whole SET of equations, one for each value of i and j.
     
  4. Jul 7, 2012 #3
    cepheid, yes of course-my mistake.

    I would like to try to list these 9 equations to make sure I understand the notation.

    SOrry, I dont have time to learn latex at the moment, but are the nine equations like this?:

    equation 1: i = 1 j = 1
    equation 2: i = 1 j = 2
    equation 3: i = 1 j = 3
    equation 4: i = 2 j = 1
    equation 5: i = 2 j = 2
    equation 6: i = 2 j = 3
    equation 7: i = 3 j = 1
    equation 8: i = 3 j = 2
    equation 9: i = 3 j = 3
     
  5. Jul 7, 2012 #4

    cepheid

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    Yeah, that looks about right to me.
     
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