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Differentiate time derivative w/ respect to generalized var.

  1. Apr 22, 2015 #1
    1. The problem statement, all variables and given/known data
    Solve ∂v/∂θ and ∂v/∂r. (refer to attached image for equations)

    2. Relevant equations
    Refer to attached image. note that the velocity is expressed in cylindrical coordinates and attention must be paid to the directional unit vectors eθ and eρ.


    3. The attempt at a solution
    Have solution (refer to attached image). However would like to understand the general steps involved such to apply them to other equations with generalised variables and time derivatives.

    If any additional information is required to solve please do not hesitate to ask.
     

    Attached Files:

  2. jcsd
  3. Apr 22, 2015 #2

    robphy

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    It looks like you took ##\frac{\partial v}{\partial \dot\theta}## and ##\frac{\partial v}{\partial \dot r}##, not ##\frac{\partial v}{\partial \theta}## and ##\frac{\partial v}{\partial r}##.

    Can you express ##\hat e_\rho## and ##\hat e_\theta## in terms of ##\hat x## and ##\hat y##?
     
  4. Apr 26, 2015 #3
    1)Yes you are correct, I made that mistake.

    2)Here are the cylindrical unit vectors expressed in Cartesian unit vectors.

    converting_cylindrical_to_cartesian.png

    C=Asinθ+Bcosθ
    D=Acosθ-Bsinθ

    Unit vectors, therefore A=B=1;

    C=sinθ+cosθ
    D=cosθ-sinθ
     
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