Motion of a spherical vibration-driven robot in a viscous fluid

Vibration-driven robot is a two-component system consisting of a solid shell placed in a viscous fluid and a movable internal mass oscillating inside it. Since such a system is not closed, the total rate of change of the momentum of its components is balanced by the hydrodinamic forces acting on the shell from the fluid. See also article "A Numerical Study of a Vibration-Driven Mechanism of Propulsion in a Viscous Fluid" https://www.researchgate.net/publication/339256888_A_Numerical_Study_of_a_Vibration-Driven_Mechanism_of_Propulsion_in_a_Viscous_Fluid