Some Methods of Analysis of the Dynamic Systems with the Various Dissipation in Dynamics of a Rigid Body

Шамолин, М. В.

doi:10.1002/pamm.200810137

Cited by 15 publications

(33 citation statements)

References 3 publications

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“…As already mentioned, one of the goals of the present study is to extend findings in the dynamics of plane-parallel motion of a body to spatial motion, i.e., to confirm the following negative answer to the question about limited-amplitude oscillations [10,12]. The quasistationary description of the interaction of a medium with a axisymmetric body moving translationally (the functions R and s (or F) depend on the angle of attack alone) produces no oscillatory solutions of finite (limited) amplitude for any admissible pair of functions R( ) a and s( ) a (or F ( ) a ) over the entire range (0 2 < < a p/ ) of finite angles of attack.…”

Section: Nonlinear Analysis (Finite Angles Of Attack)mentioning

confidence: 69%

“…This is why we "immerse" (as in [12,13]) the problem in a wider class of problems that takes into account only the qualitative properties of the functions F ( ) a (or R( ) a and s( ) a ).…”

Section: "Immersion" Of the Problem In A More General Class Of Problementioning

confidence: 99%

“…(a more general condition for the function T = |T| may also be used [12][13][14]), then an independent subsystem may be separated from the closed system of dynamic equations, as in the case of free deceleration. As a first step, we rearrange system (1.…”

Section: Closed System Of Equations Of Motionmentioning

confidence: 99%

“…In the general case, system (4.2)-(4.5), (4.10) is not integrable in terms of elementary functions because it is reduced to the Riccati equations [10,12].…”

Section: Complete Set Of Transcendental First Integralsmentioning

confidence: 99%

“…x y z 0 0 0 , q, y, j) are cyclic, which reduces the order of the dynamic system [10][11][12][13][14][15].…”

Section: Quasistationarity Hypothesismentioning

confidence: 99%

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Spatial motion of a rigid body in a resisting medium

Шамолин

2010

Int Appl Mech

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The paper studies the spatial motion of a rigid body in a resisting medium under the action of a follower force that causes the center of mass to move rectilinearly and uniformly. The body, which is axisymmetric and homogeneous, interacts with the medium by its frontal area that has the form of a flat circular disk. Since there is no exact analytic description of the forces and torques exerted by the medium on the disk, the problem is "immersed" in a wider class of problems. Partial solutions and phase portraits in the three-dimensional space of quasivelocities are obtained for the dynamic systems under consideration. The transcendental first integrals of the dynamic part of the equations of motion are listed

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Section: Nonlinear Analysis (Finite Angles Of Attack)mentioning

confidence: 69%

“…This is why we "immerse" (as in [12,13]) the problem in a wider class of problems that takes into account only the qualitative properties of the functions F ( ) a (or R( ) a and s( ) a ).…”

Section: "Immersion" Of the Problem In A More General Class Of Problementioning

confidence: 99%

Section: Closed System Of Equations Of Motionmentioning

confidence: 99%

“…In the general case, system (4.2)-(4.5), (4.10) is not integrable in terms of elementary functions because it is reduced to the Riccati equations [10,12].…”

Section: Complete Set Of Transcendental First Integralsmentioning

confidence: 99%

“…x y z 0 0 0 , q, y, j) are cyclic, which reduces the order of the dynamic system [10][11][12][13][14][15].…”

Section: Quasistationarity Hypothesismentioning

confidence: 99%

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Spatial motion of a rigid body in a resisting medium

Шамолин

2010

Int Appl Mech

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Stability of a rigid body translating in a resisting medium

Шамолин

2009

Int Appl Mech

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The paper discusses a nonlinear model that describes the interaction of a rigid body with a medium and takes into account (based on experimental data on the motion of circular cylinders in water) the dependence of the arm of the force on the normalized angular velocity of the body and the dependence of the moment of the force on the angle of attack. An analysis of plane and spatial models (in the presence or absence of an additional follower force) leads to sufficient stability conditions for translational motion, as one of the key types of motions. Either stable or unstable self-oscillation can be observed under certain conditions Keywords: rigid body in a resisting medium, nonlinear model, sufficient stability conditions, stable and unstable self-oscillation 1. Introduction. Experimental data on the motion of homogeneous circular cylinders in water [7,12] show that the dependence of the moment of force of the medium on the angular velocity of the body should also be taken into account. Then the equations of motion will include additional terms describing dissipation in the system.The nonlinear analysis of the motion of a body with finite angles of attack concentrates on establishing the conditions under which there exist finite-amplitude oscillations near the unperturbed motion, which confirms the necessity of a comprehensive nonlinear analysis. Studies of the plane and spatial models describing the interaction of a rigid body and a medium (in the presence or absence of an additional follower force) have established sufficient stability conditions for translational motion, which is a key type of motion. It was shown that there are conditions under which stable or unstable self-oscillatory motion is possible.Since the nonlinear analysis is complex, the initial stage of such a study disregards the dependence of the moment of force of the medium on the angular velocity of the body and considers the dependence on the angle of attack alone [9,11,16].Of practical importance is the stability analysis of the so-called unperturbed (translational) motion such that the velocities of points of the body are perpendicular to the plate (cavitator).All the results obtained under this elementary assumption allows concluding that there no conditions under which the systems would have solutions describing angular finite-amplitude oscillations of the body.The present paper is the next stage in the study of a moving rigid body interacting with the medium only by the flat front area (plate). The force exerted by the medium is found using the properties of a quasistationary jet flow [9]. The motion of the medium is not studied, and the characteristic time of motion of the rigid body relative to the center of mass is commensurable with the characteristic time of motion of this center.2. Plane-Parallel Motion of a Symmetric Rigid Body in a Resisting Medium: Problem Statement. Let a homogeneous rigid body of mass m undergo plane-parallel motion in a homogeneous flow of a medium. A portion of the outside

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Variety of Integrable Cases in Dynamics of Low- and Multi-Dimensional Rigid Bodies in Nonconservative Force Fields

Шамолин

2014

J Math Sci

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Some Methods of Analysis of the Dynamic Systems with the Various Dissipation in Dynamics of a Rigid Body

Cited by 15 publications

References 3 publications

Spatial motion of a rigid body in a resisting medium

Spatial motion of a rigid body in a resisting medium

Stability of a rigid body translating in a resisting medium

Variety of Integrable Cases in Dynamics of Low- and Multi-Dimensional Rigid Bodies in Nonconservative Force Fields

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