The contol of the motion through an ideal fluid of a rigid body by means of two moving masses

Kilin, Alexander A.; Vetchanin, Evgeny V.

doi:10.20537/nd1504001

Cited by 10 publications

(2 citation statements)

References 16 publications

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“…In practice, this can be achieved by means of various mechanisms such as eccentrics and sliders placed inside the body. Such control mechanisms were discussed in the problem of the planar motion of a rigid body in an ideal fluid [8,4,6,7,3,48]. The study of the problem at hand, as opposed to the above-mentioned problem, reveals much more new dynamical effects due to the absence of an additional integral of motion (similar to angular momentum).…”

Section: Introductionmentioning

confidence: 99%

The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration

2017

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This paper is concerned with the Chaplygin sleigh with timevarying mass distribution (parametric excitation). The focus is on the case where excitation is induced by a material point that executes periodic oscillations in a direction transverse to the plane of the knife edge of the sleigh. In this case, the problem reduces to investigating a reduced system of two first-order equations with periodic coefficients, which is similar to various nonlinear parametric oscillators. Depending on the parameters in the reduced system, one can observe different types of motion, including those accompanied by strange attractors leading to a chaotic (diffusion) trajectory of the sleigh on the plane. The problem of unbounded acceleration (an analog of Fermi acceleration) of the sleigh is examined in detail. It is shown that such an acceleration arises due to the position of the moving point relative to the line of action of the nonholonomic constraint and the center of mass of the platform. Various special cases of existence of tensor invariants are found.

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Section: Introductionmentioning

confidence: 99%

The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration

2017

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“…For instance, a theoretical proof of the propulsion of a body by moving the internal masses is given in [21]. The results of [21] are extended in [18,20]. Another method of moving the body involves changing the gyrostatic momentum using the rotation of internal rotors.…”

Section: Introductionmentioning

confidence: 99%

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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Rectilinear Periodic Motions of Systems with Internal Bodies

Chernousko,

Bolotnik

2024

Dynamics of Mobile Systems With Controlled Configuration

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The contol of the motion through an ideal fluid of a rigid body by means of two moving masses

Cited by 10 publications

References 16 publications

The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration

The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration

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

Rectilinear Periodic Motions of Systems with Internal Bodies

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