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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: can be written,
since:
with: or (the derivatives are taken with respect to theta). |

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: can be written:
or: which integrates to i.e. . |

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© Robert FERRÉOL
2017