ytht100
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I have the following equations:
\left\{ \begin{array}{l}<br /> x = \sin \theta \cos \varphi \\<br /> y = \sin \theta \cos \varphi \\<br /> z = \cos \theta<br /> \end{array} \right.
Assume \vec r = (x,y,z), which is a 1*3 vector. Obviously, x, y, and z are related to each other. Now I want to calculate \frac{{\partial \vec r}}{{\partial z}}, could you please tell me if you have any hint?
I have Googled the questions a lot with different terms but can't find an answer that I am sure of. Many thanks for your attention!
Attempt 1: The problem seems related to coordinate transformation between spherical and cartesian coordinates.
Attempt 2: The problem seems related to "The Cartesian partial derivatives in spherical coordinates" shown here: http://mathworld.wolfram.com/SphericalCoordinates.html.
\left\{ \begin{array}{l}<br /> x = \sin \theta \cos \varphi \\<br /> y = \sin \theta \cos \varphi \\<br /> z = \cos \theta<br /> \end{array} \right.
Assume \vec r = (x,y,z), which is a 1*3 vector. Obviously, x, y, and z are related to each other. Now I want to calculate \frac{{\partial \vec r}}{{\partial z}}, could you please tell me if you have any hint?
I have Googled the questions a lot with different terms but can't find an answer that I am sure of. Many thanks for your attention!
Attempt 1: The problem seems related to coordinate transformation between spherical and cartesian coordinates.
Attempt 2: The problem seems related to "The Cartesian partial derivatives in spherical coordinates" shown here: http://mathworld.wolfram.com/SphericalCoordinates.html.
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