Control of the motion of a cylindrical body in a viscous medium for optimal energy consumption (Q1370043)

Displacements of a cylindrical body in a viscous medium are considered, with a view to determining the optimal displacements, in the sense of minimum energy consumption, for a given time and distance. An Euler-Lagrange variational procedure is used to find the necessary optimum conditions, formulated as differential equations for local phases of the optimal motion of the cylinder. Using these equations, it can be shown that the problem has two extremal solutions. The first corresponds to motion of the cylinder at constant velocity, preserving its vertical orientation. The second involves an intermediate stage during which the cylinder is moving in a horizontal position.