Mathematical model of the motion of a body through a border of multiphase media
Investigations of the physical objects and phenomena is an interesting and complex task. This is especially true in regard to the cybernation of scientific research. This paper deals with a model of a cylindrical body displacements through border of two viscous media. The model enables one to set up the problem of displacements of a cylindrical body for optimum energy consumption, the time and distance of the displacement being given. The problem has a number of special features. First, it is irregular [Krasovskii, 1968], because the Euler–Lagrange equations do not contain controls in an explicit form, and, hence, the optimal controls cannot be determined in terms of the state and adjoint variables. Second, as it was found out, there are impulse components in the control forces and momentums optimum programs. Therefore, the classical variational techniques cannot be directly applied to find these programs. The third feature follows from the second one and consists of calculating the energy consumption. So we consider a new problem from the viewpoint of the theory of singular or degenerate [Gurman, 1985] solutions of dynamic optimization problems. CYBERNETICS AND PHYSICS, Vol. 1, No. 3, 2012 , 223–226.