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Lecture 2: Coordinate Systems and Transformation
Cartesian Coordinate System
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Cylindrical Coordinate System
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Spherical Coordinate System
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Point Transformation (Cartesian-Cylindrical Spherical)
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Constant Surfaces
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Vector Transformation (Cartesian-Cylindrical Spherical)
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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.
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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.
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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
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Example 2.4
( ) zD x y a= +
, find its expression in a cylindrical coordinate system.
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Example 2.5 ( ) zD x y a= +
, find its expression in spherical coordinate system, and vice versa.