Coordinate_Transformation_Formula_Sheet

Coordinate_Transformation_Formula_Sheet - Coordinate...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Coordinate Transformation Formula Sheet Table with the Del operator in rectangular, cylindrical, and spherical coordinates Operation Cartesian coordinates (x,y,z) Cylindrical coordinates ( ρ , φ ,z) Spherical coordinates (r, θ , φ ) Definition of coordinates ˆ ˆˆ cos sin ˆ sin cos φ φφ =+ =− + = ρ xy zz Definition of unit vectors ˆ ˆ sin cos sin sin ˆ ˆ cos cos cos sin sin ˆ sin cos θ φθ + + rx y z θ x y z ˆ sin cos ˆ ˆ ˆ cos sin = + = r ρ z θρ z
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 A vector field Gradient Divergence Curl Laplace operator Vector Laplacian Differential displacement Differential normal area
Background image of page 2
3 Differential volume Non-trivial calculation rules: 1. 2. 3. 4. 5.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 Vector Transformations in Rectangular, Cylindrical, and Spherical Coordinates From rectangular to cylindrical: cos sin 0 sin 0 00 1 x y zz AA ρ φ φφ ⎛⎞ ⎜⎟ =− ⎝⎠ From cylindrical to rectangular: sin 0 sin 0 1 x y =
Background image of page 4
5 From rectangular to spherical: sin cos sin sin cos cos
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

Coordinate_Transformation_Formula_Sheet - Coordinate...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online