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Minimal Surface between two different coaxial circules

  1. Apr 14, 2015 #1
    Dear All,

    I am trying do find the minimal surface of revolution between two coaxial circular rings of DIFFERENT diameter.

    I could not find it solved in the net. So I tried to solve numerically system (13-14) Minimal Surface of Revolution -- from Wolfram MathWorld
    to determine "a" and "b" for given coordinates did not work I got complex solutions...

    If anyone knows where I can find the solution of this problem or if anyone can give more info on this will be grate.

  2. jcsd
  3. Apr 14, 2015 #2


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    It depends upon the spacing between the rings. If they are close enough, the solution is a hyperbolic cosine curve (IIRC), but if they get further apart, this solution involves too much surface energy and the solution degenerates to a film covering each circle and a line connecting them.
  4. Apr 15, 2015 #3
    Thanks for reply. Could you pleas tell me were did you red this?
  5. Apr 15, 2015 #4


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    I did not read this. I worked the problem years ago.
  6. Apr 15, 2015 #5
    Then what is this function of distance between two coaxial rings of different diameters?
  7. Apr 15, 2015 #6
    I forget, and I do not need to know at the present time. If I did, I would work it out. I suggest the same to you.
  8. Apr 16, 2015 #7
    Are you sure that you obtained closed form solution for circles which have different diameter?
    Solution for the case when circles are equal is well known and also it is in the link which is in my post.
  9. Apr 16, 2015 #8


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