Stability of Motion of Solid Bodies with Liquid-Filled Cavities by Lyapunov's Methods

Abstract

The problem of the motion of a solid body with cavities completely filled with a liquid began to attract the attention of scientists over a century ago. Two theoretical approaches to the problem of stability are known: 1) the study of the linearized equations of the perturbed motion of the system, with application of the theory of small oscillations and of the spectral theory of operators; 2) the study of the full non-linear equations of the perturbed motion with application of Lyapunov's methods. The linear theory for this problem has been substantially developed, which has achieved considerable success. It provides a quite adequate description of the motion of the system. Its conclusions have been confirmed experimentally to a certain extent. In linearizing the equations of motion, one problem lies with the point of fact replaced by another with which the former may in some cases have nothing in common. There are no criteria at present for the correlation of these two problems in the theory of small oscillations of solid bodies containing a liquid. The establishment of such criteria would be of considerable importance for substantiating the linear theory.