Control of Body Motion in an Ideal Fluid Using the Internal Mass and the Rotor in the Presence of Circulation Around the Body

Abstract

Abstract. In this paper we study the controlled motion of an arbitrary two-dimensional body in an ideal fluid with a moving internal mass and an internal rotor in the presence of constant circulation around the body. We show that by changing the position of the internal mass and by rotating the rotor, the body can be made to move to a given point, and discuss the influence of nonzero circulation on the motion control. We have found that in the presence of circulation around the body the system cannot be completely stabilized at an arbitrary point of space, but fairly simple controls can be constructed to ensure that the body moves near the given point.

The Motion of a Balanced Circular Cylinder in an Ideal Fluid Under the Action of External Periodic Force and Torque

“…In this case, unbounded propulsion of the body turns out to be possible only under the condition Γ = 0. In the case Γ = 0, the motion of the body occurs in some bounded region of the plane Oxy [40].…”

“…The motion of an ellipsoid with internal rotors in an ideal fluid in a gravitational field was considered in [41]. In [40], problems of controlling the motion of a smooth body by means of the internal mass and the rotor with constant circulation were discussed. Also in [40], analysis was made of the problem of compensation for the drift, arising due to circulation, using controls.…”

“…In [40], problems of controlling the motion of a smooth body by means of the internal mass and the rotor with constant circulation were discussed. Also in [40], analysis was made of the problem of compensation for the drift, arising due to circulation, using controls. The focus of [37] was on the problem of controlling the motion of a smooth body using the internal fly-wheel and the Flettner rotor creating variable circulation.…”

Control of the motion of an unbalanced heavy ellipsoid in an ideal fluid using rotors

“…Рассмотрим далее вопрос о стабилизации тела в конечной точке (компенсация дрейфа). Аналогичный вопрос для управляемого движения двумерного тела в присутствии цирку-ляции жидкости подробно рассмотрен в работе [8]. Оказывается справедливо следующее предложение.…”

“…Такой подход применялся, например, в работах [6,8], однако для рассмат-риваемой системы он оказывается достаточно трудоемким и требует отдельного исследования. где Q(0) -значение матрицы Q в начальный момент времени, а Ω(n, ϕ) -матрица пово-рота на угол ϕ вокруг единичного вектора n, компоненты которой определяются соотно-шениями…”