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Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, 2011, Issue 13, Pages 75–88
(Mi vchgu53)
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Mechanics
Influence of form errors of a chamber on a rotating ball stability
O. N. Dementiev Chelyabinsk State University
Abstract:
Influece of form errors of a chamber filled with a liquid on the
movement and stability of a ball, rotating in the chamber, is
studied. Two cases of the influence of a chamber form errors on the
forces, acting on the ball, are defined. The first case describes
the situation when limitations on the rotor shift are not imposed
and disturbances of the chamber form are set by spherical harmonics
not above the first order. Then the chamber of a disturbed form,
form the point of view of the reaction forces of the liquid and
their moments, does not differ from a similar spherical chamber. In
the second case disturbance of a chamber form are arbitrary and the
rotor shift is supposed small. Then the force, acting on the rotor,
depends on its displacement only, and the momentum does not depend
on shift. A chamber of any form is equivalent to an ellipsoid. A
rising here diflective moment tends to direct the angular speed
vector along the small semiaxis of the ellipsoid, i.e., a stable
position of the rotor appears.
Keywords:
influence of form, stability, fluid, rotation.
Citation:
O. N. Dementiev, “Influence of form errors of a chamber on a rotating ball stability”, Vestnik Chelyabinsk. Gos. Univ., 2011, no. 13, 75–88
Linking options:
https://www.mathnet.ru/eng/vchgu53 https://www.mathnet.ru/eng/vchgu/y2011/i13/p75
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Statistics & downloads: |
Abstract page: | 172 | Full-text PDF : | 48 | References: | 41 |
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