The symmetry of rotating fluid bodies
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Consider an incompressible fluid body (in outer space) rotating about an axis with a given angular velocity ω, and which is in equilibrium relative to the potential energy of its own gravitational field and the surface energy due to surface tension. We show that such a body possesses a plane of symmetry perpendicular to the axis of rotation such that any line parallel to the axis and meeting the body cuts it in a line segment whose center lies on the plane of symmetry. This extends an earlier result of L. Lichtenstein .
KeywordsSurface Tension Angular Velocity Line Segment Gravitational Field Liquid Drop
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