Volume of elliptic torus (help)

slicing1 shared this question 3 years ago
Answered

The slider (beta) between i.e. 45 and 60 degs determines a strip embedded by two ellipses. My request deals with the chance to compute the shown area (PP'Q'Q) and the volume of intercepted torus. Thanks in advance.

Comments (8)

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excuse, the external like-elliptic curve is not an ellipse

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Never mind! The differences of w in the middle are very slight and don't make any trouble for my purposes. Unfortunately your proposed solution (parametric way, a couple of weeks ago) is unsuitable, due to intersect line-curve failure. Thx

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To be precise, only one line performs the interception. Cheers

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Probably the post title is erroneous, should be intended as elliptic ring, like shown in attachment. I beg your pardon, forum!

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You basically need to integrate the area of the section over the interval in which the two generating functions revolve about the x-axis. Have a look at this reference, which deals with a similar problem: http://www.dm.unipi.it/syl/upload_doc/2230.INGA-Annalisa-es8.pdf or have a look here for the basics about volumes of solids of revolution using the section method http://aulascienze.scuola.z...

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in this post

https://help.geogebra.org/t...

your question is


  1. the curves in N polygons intercepted from equally spaced angles coming from the centre.

not inside two normal lines to ellipse

sometimes you get that you ask it

I think that the volume you want is integral[w*(|a(t)+b(t))|/2,t,t0,t1] being a(t) the ellipse and b(t) the other curve

i tried with maxima

saludos

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No!

Unfortunately too much details (mine) produce plenty of misunderstandings. Reference is made to the above comments. Sorry

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Area of an ellipse having axes 2a and 2b:

pi*a*b

So, calculate the difference between the big ellipse and the little ellipse to get the area of the strip

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