- #1
LSMOG
- 62
- 0
What is dx, dy and dz in spherical coordinates
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?fresh_42 said:What are ##x,y,z## in polar coordinates? Now differentiate.
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).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?
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.
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.
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.
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.
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.