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Help with contravarient vector transformation

  1. May 28, 2010 #1
    1. The problem statement, all variables and given/known data

    Let A = <2,1> be a vector with contravarient components at a point P with coordinants u1 = 1 , u2=1. Find the components a-1,a-2 (-1 and -2 are upstairs) of this vector with respect to the coordinates u-1 = sqrt((u1)^2 + (u2)^2) and u-2 = arctan(u2/u1).

    2. Relevant equations

    V^m(y) = (dy^m/dx^n) * V (x)^n

    3. The attempt at a solution

    I got the second component to be -1/2 which is correct but for the first component i keep getting 2/2^(1/2) but the answer is 3/2^(1/2).

    The derivative of u-1 wrt u1 is:

    1/2 [ (u1)^2 + (u2)^2) ]^(-1/2) * (2*u1)

    then when i plug in u1=1 and u2 = 1 you get 1/(2^(1/2)). Then i multiply that by the a1 component 2 and this is how i got my answer.

    Can anyone see where i went wrong?
  2. jcsd
  3. May 28, 2010 #2
    Remember that there is an implied summation over terms for u1 and u2 so that I think you are missing a term for u-1 with respect to u2.
  4. May 29, 2010 #3
    If i sum over the terms then multiply by 2 i get 4/(2^(1/2)).

    but i get the 3/2^(1/2) if i multiply the first term by the 2 then sum then second term.
    but i dont know why you would do it this way since it breaks the order of operations.

    also i didnt do a summation when i did the second component and i got the right answer.

    I know that there should be a summation, but im just not sure where/ when it should occurs

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