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

V. A. Vladimirov, V. V. Rumyantsev

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A linear stability analysis is presented for the equilibrium state of a rigid body with a cavity completely filled with an ideal incompressible liquid possessing surface tension. The Lyapunov technique is used to show that the system is unstable if the second variation of the potential energy is allowed to take negative values. An estimate is derived which guarantees exponential growth of the mean-square deviations from equilibrium of the particles of the body and the liquid. The analysis employs a Lyapunov functional first defined in /1/.

Original languageEnglish
Pages (from-to)474-477
Number of pages4
JournalJournal of Applied Mathematics and Mechanics
Volume53
Issue number4
DOIs
Publication statusPublished - 1989

Fingerprint

Lagrange's theorem
Rigid Body
Inversion
Cavity
Liquid
Second Variation
Linear stability analysis
Linear Stability Analysis
Lyapunov Functional
Liquids
Exponential Growth
Potential energy
Equilibrium State
Surface Tension
Mean Square
Lyapunov
Surface tension
Deviation
Unstable
Energy

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 an ideal liquid. / Vladimirov, V. A.; Rumyantsev, V. V.

In: Journal of Applied Mathematics and Mechanics, Vol. 53, No. 4, 1989, p. 474-477.

Research output: Contribution to journalArticle

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