Title
Files
Description
The spherical coordinates of a point p can be obtained by the following geometric construction. The value of r represents the distance from the point p to the origin (which you can put wherever you like). The value of ✓ is the angle between the positive z-axis and a line l drawn from the origin to p. The value of " is the angle made with the x-axis by the projection of l into the x-y plane (z = 0). Note: for points in the x-y plane, r and " (not ✓) are polar coordinates. The coordinates (r, ✓, ") are called the radius, polar angle, and azimuthal angle of the point p, respectively. It should be clear why these coordinates are called spherical. The points r = a, with a = constant, lie on a sphere of radius a about the origin. Note that the angular coordinates can thus be viewed as coordinates on a sphere. Indeed, they label latitude and longitude.
Publication Date
2012
Keywords
spherical coordinate, transformation, polar change, chapter 13
Disciplines
Physics
Recommended Citation
Torre, Charles G., "13 Spherical Coordinates" (2012). Foundations of Wave Phenomena. Book 10.
http://digitalcommons.usu.edu/foundation_wave/10
Comments
Chapter 13