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HANGING DROP OF WATER
Homemade name. |
The hanging drop of water is the surface of revolution the curvature of which is, at any point, proportional to the distance to a plane perpendicular to its axis; according to Laplace's theorem, it models the shape of a drop of water hanging at the end of a vertical circular pipe.
For a surface of revolution obtained by the rotation around Oy of the curve x = f(t), y
= g(t), the zero curvature plane being the plane perpendicular to Oy passing by O, the differential relation: with or |
The profile of the cylindrical surface the curvature of which is proportional to the distance to a plane perpendicular to its axis is a lintearia.
We can also consider the surface of revolution the curvature of which is, at any point, proportional to the distance to a plane containing its axis:
The differential relation: or: |
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© Robert FERRÉOL
2017