[PDF] Cylindrical and Spherical Coordinates PDF 9PostNotes.pdf

Cylindrical Coordinates x = r cosθ Easy Surfaces in Cylindrical Coordinates a) r =1 6 EX 3 Convert from cylindrical to spherical coordinates (1, π/2, 1)

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The circular cylindrical coordinate system is very convenient whenever we are dealing with problems having cylindrical symmetry A point P in cylindrical

[PDF] Section 26 Cylindrical and Spherical Coordinates

z = z The reserve formula from Cartesian coordinates to cylindrical coordinates follows from the conversion formula from 2D Cartesian to 2D polar coordi- nates:

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The unit vectors in the cylindrical coordinate system are functions of position It is convenient to express them in terms of the cylindrical coordinates and the unit

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Converting the cartesian coordinates of a point P from the world frame to the local one (and reciprocally) may be done in an elegant way with homogeneous

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The unit vectors in the cylindrical coordinate system are functions of position It is convenient to express them in terms of the cylindrical coordinates and the unit

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1

Cylindrical and Spherical Coordinates

2 We can describe a point, P, in three different ways.

CartesianCylindricalSpherical

Cylindrical Coordinates

2 + y 2 y = r sinθtan θ = y/x z = zz = z

Spherical Coordinates

2 + y 2 + z 2 y = ρsinφsinθtan θ = y/x z = ρcosφcosφ = 2 + y 2 + z 2 z 3

Easy Surfaces in Cylindrical Coordinates

a) r =1b) θ = π/3c) z = 4

Easy Surfaces in Spherical Coordinates

a) ρ =1b) θ = π/3c) φ = π/4 4

EX 1Convert the coordinates as indicated

a) (3, π/3, -4) from cylindrical to Cartesian. b) (-2, 2, 3) from Cartesian to cylindrical. 5

EX 2Convert the coordinates as indicated

a) (8, π/4, π/6) from spherical to Cartesian. 6 EX 3Convert from cylindrical to spherical coordinates. (1, π/2, 1) 7 EX 4Make the required change in the given equation. a) x 2 - y 2 = 25 to cylindrical coordinates. b) x 2 + y 2 - z 2 = 1 to spherical coordinates. c) ρ = 2cos φ to cylindrical coordinates. 8 EX 4Make the required change in the given equation (continued). d) x + y + z = 1 to spherical coordinates. e) r = 2sinθ to Cartesian coordinates. f) ρsin θ = 1 to Cartesian coordiantes.quotesdbs_dbs20.pdfusesText_26

[PDF] [PDF] Cylindrical and Spherical Coordinates