- #1
Ebarval
- 6
- 0
- TL;DR
- There's nowhere online that has a simple matrix transformation from a cartesian velocity vector to a spherical velocity vector
Hi all,
I can't find a single thing online that translates a cartesian velocity vector directly to spherical vector coordinate system.
If I am given a cartesian point in space with a cartesian vector velocity and I want to convert it straight to spherical coordinates without the extra steps of calculating things such as theta or d_theta/dt .
Looking at the wiki I have a few problems:
https://en.wikipedia.org/wiki/Vector_fields_in_cylindrical_and_spherical_coordinates
I tried using the first matrix formulation in the spherical coordinates section to get my spherical coordinate vector in terms of x,y,z.
Then I take the derivative with respect to time of this to find the spherical velocity vector with respect to x,y,z, dx/dt, dy/dt, dz,dt.
I input a location in space with only an x value {a,0,0} and a cartesian velocity with only y & z components {0,vy,vz} at this cartesian location.
I would expect that a this is like being at the equator of a sphere with radius a so we'd have {a, Pi/2, 0}. Then a velocity in the y and z direction only corresponds to a velocity in the -Theta and -Phi direction.
However, I am only getting a +Phi direction. What's going wrong here?
Additionally, in the wiki article, the last equation for Adot has the terms Ar_dot, Atheta_dot, & Aphi_dot. But doesn't give any formulation for them. From what I understand, perhaps what I did above is just fine r_dot, theta_dot & phi_dot. But then where are the Adots?
I can't find a single thing online that translates a cartesian velocity vector directly to spherical vector coordinate system.
If I am given a cartesian point in space with a cartesian vector velocity and I want to convert it straight to spherical coordinates without the extra steps of calculating things such as theta or d_theta/dt .
Looking at the wiki I have a few problems:
https://en.wikipedia.org/wiki/Vector_fields_in_cylindrical_and_spherical_coordinates
I tried using the first matrix formulation in the spherical coordinates section to get my spherical coordinate vector in terms of x,y,z.
Then I take the derivative with respect to time of this to find the spherical velocity vector with respect to x,y,z, dx/dt, dy/dt, dz,dt.
I input a location in space with only an x value {a,0,0} and a cartesian velocity with only y & z components {0,vy,vz} at this cartesian location.
I would expect that a this is like being at the equator of a sphere with radius a so we'd have {a, Pi/2, 0}. Then a velocity in the y and z direction only corresponds to a velocity in the -Theta and -Phi direction.
However, I am only getting a +Phi direction. What's going wrong here?
Additionally, in the wiki article, the last equation for Adot has the terms Ar_dot, Atheta_dot, & Aphi_dot. But doesn't give any formulation for them. From what I understand, perhaps what I did above is just fine r_dot, theta_dot & phi_dot. But then where are the Adots?
