Synthesis of The Theory of Motion of Solid Bodies Filled With Bulk Substances For Fault-Tolerant Identification of Their Parameters

In the article, the Lagrange equations of motion of a solid body having volumes fully or partially filled with a granular media presented in the form of an ideal liquid. To expand the possibility of applying the theory, it is assumed that the model bulk medium has a surface tension. The first integrals of these equations have been considered. Further, conditions under which there is equilibrium or stationary motion of a solid with a loose medium that are reduced to the conditions of extremality (stationarity) of the potential energy or the modified potential energy of the system are derived from the equations of motion. In practically interesting cases, the problem of the minimum change in potential energy is solved by studying the second variation of the latter, the conclusion of the expression of which is given. In the nonlinear formulation, the theorem on the instability of the equilibrium position of a body with a granular media is proved in the case when the potential energy of the system does not have a minimum in the equilibrium position.