Nonstationary Boussinesq Viscous Medium Flow for a Solid.

The translational movement in a viscous medium a homogeneous solid with a sufficiently smooth surface is considered. The center of mass moves along the curve connecting the origin of the coordinate system with a given point of space. Such motion is provided by a control force applied to the center of mass along the tangent to the curve of the trajectory. The problem is to determine the control force, under the action of which the mass center of the body at a given time reaches a predetermined point in space with minimum expenditure of energy to overcome the viscous resistance. To calculate the drag the Boussinesq approach is used. The problem does not involve any geometric restrictions on the control force. In such a situation, impulse components may appear in the composition of the optimal control force. Therefore, an attempt to solve this problem using known classical variational procedures is not correct. The original problem is reduced to an auxiliary problem that does not contain constraints on the phase coordinates and products of generalized functions. [ABSTRACT FROM AUTHOR]