What is dx, dy and dz in spherical coordinates

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  • Thread starter LSMOG
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  • #1
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What is dx, dy and dz in spherical coordinates
 

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  • #2
14,397
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What are ##x,y,z## in polar coordinates? Now differentiate.
 
  • #3
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What are ##x,y,z## in polar coordinates? Now differentiate.
Okay. Because there are many variables. x = r sinΘ cosΦ , y = r sinΘ sinΦ and z = r cos Θ, I differebtiate with respect to what variable?
 
  • #4
14,397
11,711
Okay. Because there are many variables. x = r sinΘ cosΦ , y = r sinΘ sinΦ and z = r cos Θ, I differebtiate with respect to what variable?
All. There is no 1:1 correspondence. E.g. the origin is artificial in polar coordinates, e.g. ##r=0##, and the angles? Then there has to be a restriction of valid intervals for the angles. We will have nine equations for (x,y,z) → (r,Θ,Φ).
 
  • #5
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Thanks, let me try
 
  • #6
jtbell
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In this situation, dx is the total differential of x with respect to r, θ and Φ. So look up "total differential" and see what turns up...
 
  • #7
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Okay. Thanks
 

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