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

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/.