ABOUT STABILIZATION FOR UNSTABLE ROTATION OF LAGRANGE TOP WITH CAVITY CONTAINING FLUID

Khomyak T.V., Donetsk National University, Ukraine

The possibility of stabilization for unstable rotation of the Lagrange top with ideal fluid by means of rotating rigid bodies is shown in the limits of necessary conditions of stability. One of rotating rigid bodies has a fixed point. Numerical researches of influence parameters of rotating rigid bodies on effect of stabilization are carried out.

unstable rotation, ideal fluid, rotating rigid bodies, effect of stabilization

• Savchenko A.Ya. Ustojchivost' stacionarnyh dvizhenij mehanicheskih sistem [Stability of steady motions of mechanical systems]. Kiev: Nauk. Dumka, 1977. 160 p.
• Savchenko A.Ya., Bolgrabskaya I.A., Kononykhin G.A. Ustojchivost' dvizhenija sistem svjazannyh tverdyh tel [Stability of related solids systems motion]. Kiev, Nauk. Dumka, 1991. 168 p.
• Sobolev S.L. O dvizhenii simmetrichnogo volchka s polost'ju, napolnennoj zhidkost'ju [On the motion of a symmetric top with a cavity filled with fluid]. PMTF [Journal of Applied Mechanics and Technical Physics], 1960, no. 3, pp. 20-55.
• Kononov Yu.N., Khomyak T. Ob jeffekte stabilizacii neustojchivogo vrashhenija tverdogo tela s zhidkost'ju vrashhajushhimsja tverdym telom [The effect of stabilization of unstable solid body rotation with liquid rotary solid]. Mehanika tverdogo tela [Mechanics of Solids], 2004, no. 34, pp. 161-169.
• Kononov Y.N., T.V. Khomyak On the rotation stabilization of the unstable gyroscope containing fluid by rotating the rigid body. Facta Universitatis. Series Mechanics, Automatic Control and Robotics, Serbia, 2005, vol. 4, no. 17, pp. 195-201.
• Kononov Yu.N. O dvizhenii sistemy svjazannyh tverdyh tel s polostjami, soderzhashhimi zhidkost' [On the motion of a system of connected solids with cavities containing liquid]. Mehanika tverdogo tela [Mechanics of Solids], 2000, no. 30, no. 207-216.
• .Vysockiy M.S., Pleskachevskiy Yu.M., Shimanovsky A.O. Dinamika avtomobil'nyh i zheleznodorozhnyj cistern [Dynamics of road and rail tank cars]. Obedin. In-t mashinostroenija NAN Belarusi, Minsk, Belavtotraktorostroenie, 2006. 320 p.
• Koval V.I. O dejstvitel'nosti vseh kornej harakteristicheskogo mnogochlena uravnenij pervogo priblizhenija v dinamike tverdogo tela [On the validity of all the roots of the characteristic polynomial equations of the first approximation in the dynamics of a rigid body]. Mehanika tverdogo tela [Mechanics of Solids], 1999, no. 28, pp. 130-145.