- #1
Amith2006
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- 2
Homework Statement
I have a doubt on spheroid equations. A prolate spheroid is obtained by rotating the ellipse,
X^2/a^2 + Y^2/b^2 = 1 {Here a is major axis}
about the semi-major axis a(i.e. X axis). Its equation is,
X^2/a^2 + [Y^2+Z^2]/b^2 = 1
An oblate spheroid is obtained by rotating the ellipse,
X^2/a^2 + Y^2/b^2 = 1 {Here b is major axis}
about the semi-minor axis a(i.e. X axis).Its equation is,
X^2/a^2 + [Y^2+Z^2]/b^2 = 1
The problem is that both equations are identical. What I have done is that I have taken ‘a’ always along X axis and ‘b’ always along Y axis. Is it necessary that the equations be distinguishable?
Homework Equations
X^2/a^2 + Y^2/b^2 = 1
The Attempt at a Solution
In order distinguish between the two, I will have to take ‘a’ along Y axis for one of them. Suppose I take ‘a’ along the Y axis for oblate spheroid case, the equation of the oblate spheroid is got by rotating the ellipse,
X^2/b^2 + Y^2/a^2 = 1
about the semi-minor axis ‘b’(i.e. X axis).Its equation is,
X^2/b^2 + [Y^2+Z^2]/a^2 = 1
Another way is to rotate the ellipse,
X^2/a^2 + Y^2/b^2 = 1 {Here a is major axis}
first along X axis(i.e. ‘a’) for prolate spheroid in which case the equation becomes,
X^2/a^2 + [Y^2+Z^2]/b^2 = 1
And then along Y axis(i.e. ‘b’) for oblate spheroid in which case the equation becomes,
[X^2+Z^2]/a^2 + Y^2/b^2 = 1 {Here b is major axis}
Is there a better way to this? Please help.