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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1961
Accession Number
AD0268763

Entities

People

  • J. H. Giese

Organizations

  • Ballistic Research Laboratory

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Angular Momentum
  • Differential Equations
  • Equations
  • Equations Of Motion
  • Guided Missiles
  • Jet Propulsion
  • Kinetic Energy
  • Manufacturing
  • Military Research
  • Momentum
  • Munitions
  • New York
  • North Carolina
  • Physics Laboratories
  • Rotation
  • Steady State
  • Stereolithography

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Graph Algorithms and Convex Optimization.