What is dx, dy and dz in spherical coordinates

In summary, the conversation discusses the relationship between spherical and polar coordinates and the differentiation of variables in polar coordinates. The expert suggests looking up the concept of "total differential" and provides links to Wikipedia pages for further information.
  • #1
LSMOG
62
0
What is dx, dy and dz in spherical coordinates
 
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  • #2
What are ##x,y,z## in polar coordinates? Now differentiate.
 
  • #3
fresh_42 said:
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
LSMOG said:
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
Thanks, let me try
 
  • #6
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
Okay. Thanks
 

Related to What is dx, dy and dz in spherical coordinates

1. What are the variables dx, dy, and dz in spherical coordinates?

In spherical coordinates, dx represents the change in the x-coordinate, dy represents the change in the y-coordinate, and dz represents the change in the z-coordinate.

2. How do dx, dy, and dz relate to the spherical coordinate system?

In the spherical coordinate system, dx, dy, and dz are used to represent the infinitesimal changes in the radial distance, azimuthal angle, and polar angle, respectively.

3. How are dx, dy, and dz calculated in spherical coordinates?

Dx, dy, and dz can be calculated using the equations:

dx = dr * sin(θ) * cos(ϕ)

dy = dr * sin(θ) * sin(ϕ)

dz = dr * cos(θ)

where dr is the infinitesimal change in the radial distance, θ is the polar angle, and ϕ is the azimuthal angle.

4. What is the significance of dx, dy, and dz in spherical coordinates?

Dx, dy, and dz are important in understanding the rate of change of a function in the spherical coordinate system. They help to calculate the partial derivatives and gradients of a function in terms of the radial, azimuthal, and polar directions.

5. Are dx, dy, and dz used in other coordinate systems?

Yes, dx, dy, and dz are commonly used in other coordinate systems such as cylindrical and polar coordinates. In these systems, they represent the infinitesimal changes in the radial, angular, and height coordinates, respectively.

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