Inversion of lagrange's theorem for a rigid body with a cavity containing a viscous liquid

V. A. Vladimirov, V. V. Rumyantsev

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The stability of the state of equilibrium of a rigid body with a cavity partly or completely filled with a viscous incompressible liquid possessing surface tension is cosidered in a linear form. Lyapunov's direct method is used to show that the system is unstable if the second variation of the potential energy can take negative values. A priori lower and upper bounds for the solutions, when the perturbations are increased, are obtained. The lower bound guarantees exponential growth of the deviations of the solid and liquid particles from the equilibrium state. The upper bound shows that the solutions cannot increase at more than an exponential rate. In both cases the exponents are calculated from the parameters of the equilibrium state and the initial data for the perturbation fields.

Original languageEnglish
Pages (from-to)154-163
Number of pages10
JournalJournal of Applied Mathematics and Mechanics
Volume54
Issue number2
DOIs
Publication statusPublished - 1990

Fingerprint

Lagrange's theorem
Equilibrium State
Rigid Body
Inversion
Cavity
Liquid
Perturbation
Lyapunov Direct Method
Second Variation
Linear Forms
Liquids
Exponential Growth
Potential energy
Surface Tension
Surface tension
Upper and Lower Bounds
Deviation
Unstable
Exponent
Lower bound

ASJC Scopus subject areas

  • Mechanical Engineering
  • Applied Mathematics
  • Mathematical Physics
  • Modelling and Simulation

Cite this

Inversion of lagrange's theorem for a rigid body with a cavity containing a viscous liquid. / Vladimirov, V. A.; Rumyantsev, V. V.

In: Journal of Applied Mathematics and Mechanics, Vol. 54, No. 2, 1990, p. 154-163.

Research output: Contribution to journalArticle

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