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Lecture 2: Coordinate Systems and Transformation Cartesian Coordinate System
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.
