A recent paper by one of the authors presented a new formula found experimentally for the shape of the free surface of stable vortices. In this paper we show that the given shape is the concave spinning top with the minimum moment of inertia. A new variation method is used to find this shape, since no existing method seems to cope with the Lagrangian involving r(z)4, inequality constraints and the solution with r(0) = infinity. In the process we find spinning tops with the minimum moment of inertia under various constraints.
Comments: 19 Pages.
[v1] 2016-12-13 07:37:54
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