Surface Area of an Elipsoid
I need to find the surface area of an ellipsoid
$S={dfrac{x^{2}}{a^{2}}+dfrac{y^{2}}{b^{2}}+dfrac{z^{2}}{c^{2}}=1}$,
using double integrals.
$A(S)= intint_{S} ||n|| ds$
$n$ is a normal vector of the surface $(n=dfrac{partial r}{partial x} times dfrac{partial r}{partial y} )$.
But it's impossible using the ellipsoid parametrization:
$r(x,y)=(acdot sin(x)cos(y),bcdot sin(x)sin(y),ccdot cos(x))$.
calculus multivariable-calculus
asked Nov 30 at 0:21
Nelson Junior
14
add a comment |
I need to find the surface area of an ellipsoid
$S={dfrac{x^{2}}{a^{2}}+dfrac{y^{2}}{b^{2}}+dfrac{z^{2}}{c^{2}}=1}$,
using double integrals.
$A(S)= intint_{S} ||n|| ds$
$n$ is a normal vector of the surface $(n=dfrac{partial r}{partial x} times dfrac{partial r}{partial y} )$.
But it's impossible using the ellipsoid parametrization:
$r(x,y)=(acdot sin(x)cos(y),bcdot sin(x)sin(y),ccdot cos(x))$.
calculus multivariable-calculus
asked Nov 30 at 0:21
Nelson Junior
14
The surface area of a general triaxial ellipse cannot be expressed in terms of elementary functions. See en.m.wikipedia.org/wiki/Ellipsoid#Surface_area.
– amd
Nov 30 at 1:05
add a comment |
I need to find the surface area of an ellipsoid
$S={dfrac{x^{2}}{a^{2}}+dfrac{y^{2}}{b^{2}}+dfrac{z^{2}}{c^{2}}=1}$,
using double integrals.
$A(S)= intint_{S} ||n|| ds$
$n$ is a normal vector of the surface $(n=dfrac{partial r}{partial x} times dfrac{partial r}{partial y} )$.
But it's impossible using the ellipsoid parametrization:
$r(x,y)=(acdot sin(x)cos(y),bcdot sin(x)sin(y),ccdot cos(x))$.
calculus multivariable-calculus
asked Nov 30 at 0:21
Nelson Junior
14
I need to find the surface area of an ellipsoid
$S={dfrac{x^{2}}{a^{2}}+dfrac{y^{2}}{b^{2}}+dfrac{z^{2}}{c^{2}}=1}$,
using double integrals.
$A(S)= intint_{S} ||n|| ds$
$n$ is a normal vector of the surface $(n=dfrac{partial r}{partial x} times dfrac{partial r}{partial y} )$.
But it's impossible using the ellipsoid parametrization:
$r(x,y)=(acdot sin(x)cos(y),bcdot sin(x)sin(y),ccdot cos(x))$.
calculus multivariable-calculus
calculus multivariable-calculus
asked Nov 30 at 0:21
Nelson Junior
14
asked Nov 30 at 0:21
Nelson Junior
14
asked Nov 30 at 0:21
Nelson Junior
14
asked Nov 30 at 0:21
Nelson Junior
14
asked Nov 30 at 0:21
Nelson Junior
14
14
The surface area of a general triaxial ellipse cannot be expressed in terms of elementary functions. See en.m.wikipedia.org/wiki/Ellipsoid#Surface_area.
– amd
Nov 30 at 1:05
add a comment |
The surface area of a general triaxial ellipse cannot be expressed in terms of elementary functions. See en.m.wikipedia.org/wiki/Ellipsoid#Surface_area.
– amd
Nov 30 at 1:05
The surface area of a general triaxial ellipse cannot be expressed in terms of elementary functions. See en.m.wikipedia.org/wiki/Ellipsoid#Surface_area.
– amd
Nov 30 at 1:05
The surface area of a general triaxial ellipse cannot be expressed in terms of elementary functions. See en.m.wikipedia.org/wiki/Ellipsoid#Surface_area.
– amd
Nov 30 at 1:05
add a comment |
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The surface area of a general triaxial ellipse cannot be expressed in terms of elementary functions. See en.m.wikipedia.org/wiki/Ellipsoid#Surface_area.
– amd
Nov 30 at 1:05