Stability and instability of small motions of a pendulum with a cavity filled with a system of ideal capillary fluids
published by Tishreen University
in 2014
in
and research's language is
العربية
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Abstract in English
The aim of this paper is to study the spectral problem of small motions of a pendulum with a cavity filled with a system of ideal capillary fluids when the condition of statically stable in linear approximation is valid. It is proved that this problem has a real discrete spectrum with a limit point at and the eigenvalues for this problem are successive minima of variation ratio. It is also proved that if the operator of potential energy of a system ( pendulum + a system of ideal capillary fluids )has a negative eigenvalues, then the solutions of the initial boundary value problem are instable
References used
KOPACHEVSKY,N.D; KREIN,S.G; NGO ZUY CAN. Operators Methods in Linear Hydrodynamics:Evolution and Spectral Problem.Nauka,Moscow,1989,159-181
KOPACHEVSKY,N.D; KREIN,S.G .Operator Approach in Linear Problems of Hydrodynamics Vol. 1: Self-adjoint Problems for Ideal Fluid, Birkh¨auserVerlag, Basel—Boston—Berlin, 2001,383
KOPACHEVSKY,N.D; KREIN,S.G. Operator Approach in Linear Problems of Hydrodynamics.Vol. 2: Nonself-adjoint Problems for Viscous Fluids, Birkh¨auserVerlag, Basel—Boston—Berlin, 2003, 444
KOPACHEVSKY, N.D;On oscillation of a body with a cavity partially filled withheav ideal fluid: Theorems of existence , uniqueness and stability of strong solutions, Zb.prac.Inst.mat.NANUkr, Kyiv, Vol .2,no.1,2005,158-194