QUALITATIVE ASPECTS OF THE MOTION OF RIGID BODIES WITH LIQUID-FILLED TOROIDAL CAVITIES
Abstract
For a rigid body subject to no moments, the integral curves of the differential equations for the angular velocity are intersections of the energy and angular momentum ellipsoids, which have common centers and principal axes. If the solid contains a cavity that is topologically equivalent to the interior of a sphere completely filled with non-viscous incompressible fluid, these properties remain valid. But if the cavity is topolocially equivalent to the interior of a torus, the fluid may have a non-vanishing circulation, A. The angular velocity integral curves are still intersections of ellipsoids, but one of the centers was displaced through a distance that depends on A. If A is 0 there are four types of closed integral curves; five for weak circulation; three for intermediate (Al); and one for strong (A). The qualitative nature of the integral curves for cavities of greater topological complexity is closely skin to that for toroidal cavities.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1961
- Accession Number
- AD0268763
Entities
People
- J. H. Giese
Organizations
- Ballistic Research Laboratory