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ValeryOchkov24-Ruby IV
24-Ruby IV
May 25, 2018
Question

Catenary and cone - one fresh problem for Mathcad community

  • May 25, 2018
  • 1 reply
  • 4453 views

Do you know how a catenary lies on the cone? Without friction!

Cone-and-Catenary.png

 

1 reply

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-MFra-21-Topaz II
21-Topaz II
May 25, 2018

Hi Valery,

You should be clearer because the figure shows an ellipsis. It is known to all that the intersection of a plane with a cone is a conic (in this case ellipsis precisely). Therefore I deduce that the catenary is generated by the intersection of a cone and a non-flat surface. the system between the equation of a cone and an unknown surface must give a catenary. Does this surface exist? ......but then, since the catenary is a flat curve, the surface should be a plane, which contradicts the previous deduction.

The cone is ready...........

Cono.jpg

V
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
May 25, 2018

1. Sorry, it is not a catenary (one plane curve), but a chain.

2. Better use a cylindrical system of coordinates

3. This problem has two boundary cases:

- a circle

- a part line 

Cone-12.png

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-MFra-21-Topaz II
21-Topaz II
May 25, 2018

So the problem seems trivial because the circle is given by the intersection of the cone and a plane perpendicular to the axis of the cone, while the chain is the locus of points where the plane is tangent to the cone .....

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