Dynamics of a rigid body with an ellipsoidal cavity filled with viscous fluid

We revisit the approach proposed by F.L.  Chernousko to modeling the dynamics of a rigid body with a cavity entirely filled with a highly viscous fluid. Within the approach, a finite-dimensional model of the body+fluid system is offered and the influence of the fluid is represented as a special torque acting upon the body with solidified fluid. Our aim is to develop further and expand a few technical aspects of the Chernousko model. In particular, we offer a coordinate-free form for some essential formulas and consider the case of constrained dynamics. To illustrate the results obtained we explore the motion of a physical pendulum with a fluid-filled cavity on a rotating platform.     

Oscillations of a body filled with a viscous fluid

The oscillations of a physical pendulum containing a spherical cavity filled with an incompressible viscous liquid were discussed in [1]. In this paper we consider the mote general problem of the motion of an axially symmetric solid with a spherical cavity filled with an incompressible viscous fluid and moving about a fixed point. It is assumed that the center of the cavity and the fixed point lie on the axis of symmetry of the body.     

On the stability of a flexibly mounted rotating cylinder partially filled with liquid

Summary An investigation is made into the unstable behaviour of a rotor which is flexibly mounted with some damping and which is forced to rotate around its axis of symmetry with a constant angular velocity. The rotor is assumed to be partially filled with an ideal liquid. Assuming relative liquid motion in two dimensions a perturbation theory leads to an algebraic equation of the fourth degree from which information can be derived about unstable regions and the effect of the combined action of dissipative and gyroscopic forces.     

Study of dynamic processes in a rigid cylindrical vessel with elastic bottom partially filled with a liquid

The paper reports on the results from an experimental study of the nonlinear deformation of the elastic bottom of and the free liquid surface in a rigid shell. The shell and liquid interact with each other and with a cluster of gas bubbles produced by vibrational excitation __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 114–120, November 2006.     

Numerical study of axisymmetric waves in an elastic cylindrical shell partially filled with a viscous liquid

Moscow Institute of Electronics and Mechanical Engineering. Translated from Prikladnaya Mekhanika, Vol. 24, No. 2, pp. 50–54, February, 1988.     

On the stability of the rotational motion of a rigid body having a liquid filled cavity under finite initial disturbance

In this paper the problem of the stability of rotational motion of a rigid body which has a liquid filled cavity and a fixed point is investigated without any approximation. Criteria of stability and instability under finite disturbance are obtained. The region of stability is found out explicitly.