On the stability of a top with a cavity filled with a viscous fluid. (English. Russian original) Zbl 0960.76037

Kostyuchenko, A. G.; Shkalikov, A. A.; Yurkin, M. Yu.

Funct. Anal. Appl. 32, No. 2, 100-113 (1998); translation from Funkts. Anal. Prilozh. 32, No. 2, 36-55 (1998).

The authors consider small oscillations of a heavy top with a cavity completely filled by viscous incompressible fluids. The main goal is to derive a criterion for stability of motion of this system, and to investigate spectral properties of the evolution operator. A modification of equations of motion is suggested, which is more convenient for further representation of the linear problem as operator equation in Hilbert space. The authors introduce the instability index equal to the dimension of the factor space of linear space of all solutions with respect to the space of its bounded solutions (or, equivalently, to the number of linearly independent growing solutions). The case of large viscosity is investigated separately. The approach is applied to a symmetric top, where the author identify some cases of unstable motion.

Reviewer: Oleg Limarchenko (Kyïv)

MSC:

76E99	Hydrodynamic stability
70E50	Stability problems in rigid body dynamics

Keywords:

heavy top filled by viscous incompressible fluid; evolution operator; criterion for stability of motion; spectrum; instability index; large viscosity; symmetric top; linearization; operator equation; Hilbert space

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