Free and controlled motion of a body with a moving internal mass through a fluid in the presence of circulation around the body

Vetchanin, Evgeny V.; Kilin, Alexander A.

doi:10.1134/s1028335816010110

Cited by 12 publications

(11 citation statements)

References 9 publications

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“…Свободное движение тела с циркуляцией исследовано, например, в работе [Borisov, Mamaev, 2006]. Управляемое движение тела с помощью различных внутренних механизмов с учетом циркуляции исследовалось в [Vetchanin, Kilin, 2016a;Vetchanin, Kilin, 2016b;Vetchanin, Kilin, 2017]. В данных работах была доказана полная управляемость рассматриваемой системы на фиксированном уровне первых интегралов.…”

Section: учет циркуляции жидкости вокруг телаunclassified

Controlling the movement of the body using internal masses in a viscous liquid

Kilin¹,

Klenov²,

Tenenev³

2018

CRM

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This article is devoted to the study of self-propulsion of bodies in a fluid by the action of internal mechanisms, without changing the external shape of the body. The paper presents an overview of theoretical papers that justify the possibility of this displacement in ideal and viscous liquids.A special case of self-propulsion of a rigid body along the surface of a liquid is considered due to the motion of two internal masses along the circles. The paper presents a mathematical model of the motion of a solid body with moving internal masses in a three-dimensional formulation. This model takes into account the three-dimensional vibrations of the body during motion, which arise under the action of external forces-gravity force, Archimedes force and forces acting on the body, from the side of a viscous fluid.The body is a homogeneous elliptical cylinder with a keel located along the larger diagonal. Inside the cylinder there are two material point masses moving along the circles. The centers of the circles lie on the smallest diagonal of the ellipse at an equal distance from the center of mass.Equations of motion of the system (a body with two material points, placed in a fluid) are represented as Kirchhoff equations with the addition of external forces and moments acting on the body. The phenomenological model of viscous friction is quadratic in velocity used to describe the forces of resistance to motion in a fluid. The coefficients of resistance to movement were determined experimentally. The forces acting on the keel were determined by numerical modeling of the keel oscillations in a viscous liquid using the Navier -Stokes equations.In this paper, an experimental verification of the proposed mathematical model was carried out. Several series of experiments on self-propulsion of a body in a liquid by means of rotation of internal masses with different speeds of rotation are presented. The dependence of the average propagation velocity, the amplitude of the transverse oscillations as a function of the rotational speed of internal masses is investigated. The obtained experimental data are compared with the results obtained within the framework of the proposed mathematical model.

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Section: учет циркуляции жидкости вокруг телаunclassified

Controlling the movement of the body using internal masses in a viscous liquid

Kilin¹,

Klenov²,

Tenenev³

2018

CRM

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“…In [32] the controllability of motion by means of an internal mass capable of moving arbitrarily inside the body is proved. Therefore, an analogous system to which an internal rotor is added is controllable as well.…”

Section: Controllabilitymentioning

confidence: 99%

“…The controlled motion using an internal rotor changing the proper gyrostatic momentum of the system and using a Flettner rotor changing the circulation around the body is considered in [26]. In [32], analysis of the free motion of a hydrodynamically asymmetric body in an ideal fluid in the presence of circulation is performed and the controllability of the motion by changing the position of the center of mass of the system is proved.An essential part of the investigation of the controlled motion is the proof of the possibility of control. In [6,21,25,32] the Rashevskii-Chow theorem is used to prove controllability [1].…”

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confidence: 99%

“…For example, it is of interest to construct time-optimal controls [13,14]. For various aspects of control theory, see [1,17].This paper is an extension of [32], but in contrast to the previous paper, we are concerned with a combined control scheme which uses the motion of the internal mass and rotation of the internal rotor. In Section 2, equations of motion and their first integrals are presented.…”

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confidence: 99%

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

Vetchanin

Kilin

2016

J Dyn Control Syst

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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.

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“…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…”

Section: предложение 2 компенсация дрейфа в конечной точке траекториunclassified

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

Vetchanin¹,

Kilin²

2016

Nelin. Dinam.

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Free and controlled motion of a body with a moving internal mass through a fluid in the presence of circulation around the body

Cited by 12 publications

References 9 publications

Controlling the movement of the body using internal masses in a viscous liquid

Controlling the movement of the body using internal masses in a viscous liquid

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

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

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