Stability of Steady Motion of Rigid Bodies with Fluid-Filled Cavities

Abstract

In this chapter we will consider the stability of steady motion, in particular, of equilibrium of rigid bodies with cavities partially or completely filled with ideal or viscous fluids. This study is based on the definition of stability and on the ideas developed by Lyapunov in the theory of stability of equilibrium shapes of a rotating fluid48, 55. It has been proved that the problem of the stability of steady motion or of the equilibrium of a rigid body containing a fluid reduces to the problem of minimizing a certain expression56, 57 a solution to which is given54, 58. The results are used for solving a number of problems of stability of motion of bodies containing a fluid.KeywordsFree SurfaceRigid BodyDynamic StabilityRelative EquilibriumSurface Tension ForceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.