Getting the area of a surface integral from Matlab

Question

Niklas Kurz 2021-5-5

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/822005-getting-the-area-of-a-surface-integral-from-matlab

评论： Star Strider 2021-5-5

采纳的回答： Star Strider

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I'd like to approve my solution of

where

is the unit sphere

Therefore I want to calculate

where

is the parametrization of the unit sphere:

syms phi the
x = cos(phi).*sin(the);
y = sin(phi).*sin(the);
z = cos(the);
density = x.^2;
para = [x;y;z];
dphi = diff(para,phi);
dthe = diff(para,the);
c = cross(dphi,dthe);
int(int(density*norm(c),phi,0,2*pi),the,0,pi)

Like in my previous quesion I get a cryptic answere, not really any helpfull probably because norm(c) is overcomplicated

Also is there another way to approve the solution. e.g. with trapz?

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Answer 1

Star Strider 2021-5-5

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/822005-getting-the-area-of-a-surface-integral-from-matlab#answer_692465

在 MATLAB Online 中打开

See if simplifying it does what you want —

syms phi the

x = cos(phi).*sin(the);

y = sin(phi).*sin(the);

z = cos(the);

density = x.^2;

para = [x;y;z];

dphi = diff(para,phi);

dthe = diff(para,the);

c = cross(dphi,dthe);

Int2 = int(int(density*norm(c),phi,0,2*pi),the,0,pi)

Int2 =

Int2 = simplify(Int2, 500)

Int2 =

.

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Niklas Kurz 2021-5-5

That second entry in simplify was unexpected. I should look at the documentation more extensively...

Star Strider 2021-5-5

在 MATLAB Online 中打开

No worries!

The full documentation would likely suggest —

Int2 = simplify(Int2, 'Steps',500)

Leaving out the 'Steps' name in the name-value pair is a shortened way of specifying it. Other name-value pairs require the name to be specified as well, also if more than one are specified.

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