On the dynamics of a body with an axisymmetric base sliding on a rough plane

Borisov, A. V.; Karavaev, Y. L.; Mamaev, Ivan S.; Erdakova, N. N.; Ivanova, Tatiana B.; Tarasov, V. V.

doi:10.20537/nd1503006

Cited by 7 publications

(13 citation statements)

References 42 publications

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“…In particular, it is demonstrated that in some cases the trajectories of an equilateral tripod are similar to those of a body with an annular contact area. However, a counterexample of an "undulatory" trajectory of the tripod is also given, which contradicts the well-known laws of the dynamics of bodies with a flat base [6].…”

Section: Introductionmentioning

confidence: 65%

“…We give particular attention to comparison of the laws of dynamics of a tripod and a body with a flat round base (disk); for a detailed review, analytical and experimental study of such a body see [6] and [7]. It is well known from theoretical works that the pattern of absolute motion of the disk depends on the choice of the model of the pressure distribution of the body on the plane of sliding.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a body sliding on a rough plane and supported at three points

Borisov

Mamaev

Erdakova

2016

Theor appl mech (Belgr)

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This paper is concerned with the problem of a rigid body (tripod) moving with three points in contact with a horizontal plane under the action of dry friction forces. It is shown that the regime of asymptotic motion (final dynamics) of the tripod can be pure rotation, pure sliding, or sliding and rotation can cease simultaneously, which is determined by the position of the tripod's supports relative to the radius of inertia. In addition, the dependence of the trajectory of the center of mass on the system parameters is investigated. A comparison is made with the well-known theoretical and experimental studies on the motion of bodies with a flat base.2010 Mathematics Subject Classification: 70F40, 70E18.

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Section: Introductionmentioning

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Dynamics of a body sliding on a rough plane and supported at three points

Borisov

Mamaev

Erdakova

2016

Theor appl mech (Belgr)

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“…When 1728β 3 < 27g 2 3 solution (32) becomes singular on the real line. In Fig.4 we present a plot of solution (32) for values of the parameters that satisfy 1728β 3 > 27g 2 3 . In this section we have constructed four examples of integrable Liénardtype equations along with their general solutions.…”

Section: Examplesmentioning

confidence: 99%

On the integrability conditions for a family of Liénard-type equations

Kudryashov¹,

Sinelshchikov²

2016

Regul. Chaot. Dyn.

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We study a family of Liénard-type equations. Such equations are used for the description of various processes in physics, mechanics and biology and also appear as traveling-wave reductions of some nonlinear partial differential equations. In this work we find new conditions for the integrability of this equations family. To this end we use an approach, which is bases on application of nonlocal transformations. By studying connections between this family of Liénard-type equations and type III Painlevé-Gambier equations, we obtain four new integrability criteria. We illustrate our results by providing examples of some integrable Liénard-type equations. We also discuss relationships between linearizability via nonlocal transformations of this family of Liénard-type equations and other integrability conditions for this family of equations.MSC2010 numbers: 34A05, 34A34, 34A25.

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“…Unfortunately, the problems of dynamical friction which occur during the motion are poorly understood. The few studies worth mentioning are concerned with the stability of decelerative sliding motions of a driven mechanical system [1], the motion of a cylinder on a rough plane [2], and the motion of a curling rock [3] and [4].…”

Section: Introductionmentioning

confidence: 99%

On a mechanical lens

Иванов

Erdakova

2016

International Journal of Non-Linear Mechanics

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In this paper, we consider the dynamics of a heavy homogeneous ball moving under the influence of dry friction on a fixed horizontal plane. We assume the ball to slide without rolling. We demonstrate that the plane may be divided into two regions, each characterized by a distinct coefficient of friction, so that balls with equal initial linear and angular velocity will converge upon the same point from different initial locations along a certain segment. We construct the boundary between the two regions explicitly and discuss possible applications to real physical systems

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On the dynamics of a body with an axisymmetric base sliding on a rough plane

Cited by 7 publications

References 42 publications

Dynamics of a body sliding on a rough plane and supported at three points

Dynamics of a body sliding on a rough plane and supported at three points

On the integrability conditions for a family of Liénard-type equations

On a mechanical lens

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