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"Prolate spheroidal coordinates" are a set of coordinates for Håt are: I= Rsinh x sin ở cos o, y= Rsinh x sin ở sin o, z= Rcosh y cos e, where we fix R to have dimensions of length and take R= 1 AU (AU-astronomical unit). Consider the plane y = = dy = = 0. (a) Find the transformation matrix Or"/əz" relating the z, z coordinates to the x,e coordinates? (b) Write the line element, ds in x,0 coordinates. %3D Give numerical answers for (a) and (b) at the point = 2.1, x = 3.4.

"Prolate spheroidal coordinates" are a set of coordinates for Håt are: I= Rsinh x sin ở cos o, y= Rsinh x sin ở sin o, z= Rcosh y cos e, where we fix R to have dimensions of length and take R= 1 AU (AU-astronomical unit). Consider the plane y = = dy = = 0. (a) Find the transformation matrix Or"/əz" relating the z, z coordinates to the x,e coordinates? (b) Write the line element, ds in x,0 coordinates. %3D Give numerical answers for (a) and (b) at the point = 2.1, x = 3.4.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 97E
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"Prolate spheroidal coordinates" are a set of coordinates for flat three dimensional Euclidean space. They are: I = Rsinh x sin 0 cos , y = Rsinh x sin 0 sin ø̟, z = Rcosh x cos 0, where we fix R to have dimensions of length and take R = 1 AU (AU=astronomical unit). Consider the plane y = dy = $ = 0. (a) Find the transformation matrix dr"/az" relating the a, z coordinates to the x, 0 coordinates? (b) Write the line element, ds in x,0 coordinates. %3D Give numerical answers for (a) and (b) at the point 60 = 2.1, x=3.4. %3D
Transcribed Image Text:"Prolate spheroidal coordinates" are a set of coordinates for flat three dimensional Euclidean space. They are: I = Rsinh x sin 0 cos , y = Rsinh x sin 0 sin ø̟, z = Rcosh x cos 0, where we fix R to have dimensions of length and take R = 1 AU (AU=astronomical unit). Consider the plane y = dy = $ = 0. (a) Find the transformation matrix dr"/az" relating the a, z coordinates to the x, 0 coordinates? (b) Write the line element, ds in x,0 coordinates. %3D Give numerical answers for (a) and (b) at the point 60 = 2.1, x=3.4. %3D
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