how to convert from rectangular coordinates to spherical coordinates?

Question

amistre64 · Answer

spherical coordinantes or polar coordinantes?

amistre64 · Answer

I spose if the "rectangular" system is (x,y,z) axis that we could convert it to spherical....

amistre64 · Answer

x = r cos(t)

y = r sin(t)

z = ..... r cos(w) ??  dunno what to make for the z :)

anonymous · Answer

Theta is the same.  x=rho*sin phi*cos theta, y=rho*sin phi *sin theta, z=rho*cos phi, r=rho*sin phi

anonymous · Answer

Also, rho^2=x^2+y^2+z^2.  Phi is the angle that rho makes with the positive z axis, 0<=rho<=pi.  So, it usually isn't much trouble going from rectangular to polar or cylindrical and then to sperical.

mendicant_bias · Answer

Amistre; just remarking:

My book (and several others, I feel like somebody would have a better name by now) refers to 3-dimensional, xyz coordinate systems, as "rectangular coordinate" systems. Despite both spherical and cylindrical being named after exclusively 3-dimensional objects.

mendicant_bias · Answer

"Rectangular cuboid, right cuboid, rectangular box, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped" don't ring very well.

Something like "prismatic coordinates" or "prism coordinates" sounds cool but makes an unsaid assumption that you are dealing with right rectangular prisms.