Stabilization of a Spinning Lagrange Gyroscope Filled with Ideal Fluid in a Resisting Medium

The possibility of stabilizing the unstable uniform rotation of the “sleeping” Lagrange gyroscope filled with an ideal fluid in a resisting medium by a second spinning gyroscope and elastic spherical joints is shown. The “sleeping” gyroscope contains an arbitrary axisymmetric cavity completely fille...

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Bibliographic Details
Published in:International applied mechanics 2023-03, Vol.59 (2), p.207-217
Main Authors: Kononov, Yu. M., Svyatenko, Ya. I.
Format: Article
Language:English
Subjects:
Angular speed
Applications of Mathematics
Elastic properties
Engineering
Fluid flow
Gyroscopes
Ideal fluids
Incompressible flow
Incompressible fluids
Rotation
Stabilization
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Summary:The possibility of stabilizing the unstable uniform rotation of the “sleeping” Lagrange gyroscope filled with an ideal fluid in a resisting medium by a second spinning gyroscope and elastic spherical joints is shown. The “sleeping” gyroscope contains an arbitrary axisymmetric cavity completely filled with an ideal incompressible fluid and spins around a fixed point. Positioned above the first gyroscope, the second gyroscope is connected to it via an elastic spherical joint. Constant torques directed along the axes of symmetry of the gyroscopes sustain their rotations. By determining appropriate conditions for the elasticity coefficients of the joints, the first tone of oscillations of the ideal fluid, and the centers of mass of the gyroscopes, it becomes feasible to achieve stabilization. To illustrate this, a compressed ellipsoidal cavity is considered. In this case, stabilization is always attainable provided the angular speed of rotation of the second gyroscope is sufficiently high and the center of mass of the second gyroscope is positioned below the common point of the gyroscopes. The resulting stabilization conditions are compared with similar conditions in the absence of dissipation.
ISSN:1063-7095
1573-8582
DOI:10.1007/s10778-023-01213-1