What is Spherical coordinates? — Physics

Definition 11.10 University Physics — Year 1 · Chapter 11 — Kinematics of a Point

Point $M$ is located by its distance $r = OM$ , the colatitude $\theta \in [0, \pi]$ between $\vect{OM}$ and $\vect e_z$ , and the azimuth $\varphi$ of its projection on the $xy$ plane: $\vect{OM} = r\,\vect e_r$ with

\vect e_r = \sin\theta\cos\varphi\,\vect e_x + \sin\theta\sin\varphi\,\vect e_y + \cos\theta\,\vect e_z ;

$\vect e_\theta$ (tangent to the meridian, toward increasing $\theta$ ) and $\vect e_\varphi$ (tangent to the parallel) complete the local orthonormal basis. On the Earth, $\theta$ is $90^\circ$ minus the latitude and $\varphi$ the longitude.

Spherical coordinates (r, , ) and their local basis: e_r radial, e_ along the meridian (toward the south on a globe), e_ along the parallel (toward the east). — Spherical coordinates $(r, \theta, \varphi)$ and their local basis: $\vect e_r$ radial, $\vect e_\theta$ along the meridian (toward the south on a globe), $\vect e_\varphi$ along the parallel (toward the east).

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