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Notation for Velocity Gradient

  • Thread starter swmmr1928
  • Start date
  • #1
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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.

Homework Statement



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

Homework Equations



8VDbY.jpg

Source: Stanley Middleman

The Attempt at a Solution



My confusion is with the 1/2 and the subscripts used.
 

Answers and Replies

  • #2
cepheid
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Science Advisor
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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.
 
  • #3
55
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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
 
  • #4
cepheid
Staff Emeritus
Science Advisor
Gold Member
5,192
35
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
Yeah, that looks about right to me.
 

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