Velocity in spherical polar coordinates

In summary, the conversation discusses the confusion surrounding the definition of r, theta, and phi in the derivation of velocity in spherical polar coordinates. The introduction of equations from other disciplines and the use of different spherical coordinate systems can lead to booby traps and confusion. The substitution of latitude for colatitude may also change the equation.
  • #1
meteo student
72
0
I am looking at this derivation of velocity in spherical polar coordinates and I am confused by the definition of r, theta and phi.
http://www.usna.edu/Users/math/rmm/SphericalCoordinates.pdf

I thought phi was the co latitude in the r,θ,∅ system and not the latitude. Of course the two are related through the equation 90 - colatitude.

Would this change the derivation ?
 
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  • #2
Hello weatherstudent, :welcome:

It's a choice that looks convenient for looking at the world with its historically grown coordinnate system.
Derivation doesn't change, but you want to be careful bringing in equations from other disciplines; you'll have a minus sign here and there, or the range of ##\phi## may cause confusion.

Physicists and and mathematicians also have created their own booby traps by adapting different spherical coordinate systems, so why shouldn't meteorologists have yet another one :smile: !
 
  • #3
Thanks for that response and the welcome. :-)

I wasn't referring to the convenience. Would substituting latitude for colatitude not change the equation as well ?
 

Related to Velocity in spherical polar coordinates

1. What is velocity in spherical polar coordinates?

Velocity in spherical polar coordinates is a way of measuring the speed and direction of an object in three-dimensional space. It uses three coordinates, known as radial distance, azimuthal angle, and polar angle, to describe the position and movement of the object.

2. How is velocity in spherical polar coordinates different from velocity in Cartesian coordinates?

In Cartesian coordinates, velocity is described using three coordinates: x, y, and z. In spherical polar coordinates, velocity is described using three different coordinates: radial distance, azimuthal angle, and polar angle. This allows for a more intuitive understanding of the object's movement in three-dimensional space.

3. How do you convert velocity from spherical polar coordinates to Cartesian coordinates?

To convert velocity from spherical polar coordinates to Cartesian coordinates, you can use the following equations:
x = r * sin(θ) * cos(ϕ)
y = r * sin(θ) * sin(ϕ)
z = r * cos(θ)
where r is the radial distance, θ is the polar angle, and ϕ is the azimuthal angle.

4. What is the significance of the radial distance in velocity in spherical polar coordinates?

The radial distance in velocity in spherical polar coordinates represents the distance of the object from the origin point. It is important because it allows us to track the movement of the object in relation to the origin point, and it is also used in the conversion to Cartesian coordinates.

5. How is velocity in spherical polar coordinates used in physics?

Velocity in spherical polar coordinates is commonly used in physics to describe the movement of objects in three-dimensional space. It is especially useful in situations where the object is moving in a circular or spherical path, as it allows for a more accurate representation of its velocity and direction of motion.

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