Nonlinear Oscillations of a Mechanical System with Two Fluids in Motion of a Rigid Body

The mechanical model of a system with a spherical pendulum corresponding to nonlinear oscillations of the interface between two fluids, that completely occupy a cylindrical vessel, during translational and rotational motions of a rigid body, is considered. The amplitude–frequency characteristics are used to analyze and compare the behavior of the mechanical model with the real system in more detail. Numerical calculations of the linear and nonlinear coefficients of the equations that describe the translational and rotational motions of the rigid body at various depths of each of the fluids are also carried out. It is shown that when the direction cosines are taken as generalized coordinates that define the position of the spherical pendulum, then the equations of motion of the equivalent mechanical analog correspond to the dynamics equations for a rigid body with two fluids up to the second order of smallness. As a result, the amplitude–frequency characteristics and instability regions of forced vibrations of the interface between liquids with different densities and levels in a cylindrical vessel during translational and angular motions of the rigid body are constructed.