Cartesian Coordinate Systemdjiao/ee311/classnote/Lecture2.pdf · Example 2.2 . Find the coordinates...

Lecture 2: Coordinate Systems and Transformation

Cartesian Coordinate System

Cylindrical Coordinate System

Spherical Coordinate System

Point Transformation (Cartesian-Cylindrical Spherical)

Constant Surfaces

Vector Transformation (Cartesian-Cylindrical Spherical)

Example 2.1 Find the coordinates of point P(2, 2, 3) in the cylindrical coordinate system.

Find the coordinates of point P(1, 30o, 3) in the rectangular coordinate system.

Example 2.2 Find the coordinates of point P(2, 2, 3) in the spherical coordinate system. Find the coordinates of point P(2, 30o, 60o) in the rectangular coordinate system.

Example 2.3

(1) The intersection between x=3 and z=0 is (2) The intersection between x=3, y=5, and z=0 is

(3) The intersection between 2ρ = and 60oϕ = is

(4) The intersection between 2ρ = and z=0 is

(5) The intersection between 45oϕ = and z=0 is

(6) The intersection between 2r = and 60oϕ = is

(7) The intersection between 2r = and 60oθ = is

(8) The intersection between 60oθ = and 45oϕ = is

Example 2.4

( ) zD x y a= +

, find its expression in a cylindrical coordinate system.

Example 2.5 ( ) zD x y a= +

, find its expression in spherical coordinate system, and vice versa.