The movement of a disc on a rotating horizontal plane with dry friction

Karapetyan, A.V.

doi:10.1016/j.jappmathmech.2017.02.003

Cited by 4 publications

(5 citation statements)

References 2 publications

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“…11 − 2bmn A (3) 22 + b(m 2 − n 2 + 4b 2 )A (4) 22 + 2bmn A (3) 11 ] + (3A (1) 13 + A 11 + 4mnb(m 2 + n 2 )A (4) 12 + 2b 2 n(4b 2 + 3m 2 − n 2 )A (4) 22 ] + (3A (1) 14 + A (2) 24 )[2b 2 n(3n 2 − m 2 − 4b 2 )A (3) 11 − n(m 2 + n 2 ) 2 A (3) 11 − 4mnb(m 2 + n 2 )A (3) 12 − 2b 2 n(3m 2 + 4b 2 − n 2 )A (3) 22 + m(m 2 + n 2 )(m 2 + n 2 + 6b 2 )A (4) 11…”

Section: A1 Transformation To Jordan Normal Formunclassified

“…11 − 2b(m 2 + n 2 )(n 2 − m 2 − 4b 2 )A (4) 12 + 2b 2 m(m 2 − 3n 2 + 4b 2 )A (4) 22 ] + (3A (2) 23 + A 12 − 2nb 2 (3n 2 − m 2 − 4b 2 )A (4) 22 + n(m 2 + n 2 ) 2 A (4) 22 ] + (3A (2) 24 + A (1) 14 )[4bmn(m 2 + n 2 )A (3) 12 − 2b 2 n(3m 2 + 4b 2 − n 2 )A (3) 11 − n(m 2 + n 2 ) 2 A…”

Section: A1 Transformation To Jordan Normal Formunclassified

“…The motion of bodies on surfaces is a classical problem of mechanics [1,2] and was investigated in various statements (see, for example, [3][4][5][6]). In the most simple case, a point particle instead of a rigid body could be considered.…”

Section: Introductionmentioning

confidence: 99%

“…13 )[2b 2 m(4b 2 + m 2 − 3n 2 )A (3) 11 − 2b(m 2 + n 2 )(m 2 − n 2 + 4b 2 )A (32b 2 m(n 2 − 4b 2 − 3m 2 )A (3) 22 + m(m 2 + n 2 ) 2 A (3)22 + 2b 2 n(4b 2 + 3m 2 − n 2 )A (44bmn(m 2 + n 2 )A(4) …”

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On Hopf bifurcation in the problem of motion of a heavy particle on a rotating sphere: the viscous friction case

2019

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We investigate the Hopf bifurcation of a mass on a rotating sphere under the influence of gravity and viscous friction. After determining the equilibria, we study their stability and calculate the first Lyapunov coefficient to determine the post-critical behavior. It is found that the bifurcating periodic branches are initially stable. For several inclination angles of the sphere's rotation axis, the periodic solutions are calculated numerically, which shows that for large inclination angles turning points occur, at which the periodic solutions become unstable. We also investigate the limiting case of small friction coefficients, when the mass moves close to the equator of the rotating sphere.

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Section: A1 Transformation To Jordan Normal Formunclassified

Section: Introductionmentioning

confidence: 99%

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On Hopf bifurcation in the problem of motion of a heavy particle on a rotating sphere: the viscous friction case

2019

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“…In this case, the trajectory is unlimited. In [8], the problem of the dynamics of a flat disk on a rotating plane was studied.…”

Section: Introductionmentioning

confidence: 99%

On the Dynamics of a Biped upon a Moving Rough Plane

Ivanov

2024

Nelin. Dinam.

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We consider the planar problem of the dynamics of a body moving along a horizontal with two legs in contact with a rough horizontal plane. Possible types of movements of the body are discussed depending on the acceleration of the support: relative equilibrium, sliding on two legs, lifting off one leg without sliding on the other, lifting off one leg while sliding on the other. Based on the results obtained, it is shown that, when sliding on two legs, the friction force is generally anisotropic. This makes it possible to transport the body due to simple vibrations of the plane, for example, harmonic vibrations.

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Harmonic expansion and nonsmooth dynamics in a circular contact region with combined slip-spin motion

Antali

2024

Nonlinear Dyn

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We analyse a rigid body in planar motion while touching a rough plane at a finite-sized, circular contact area. Assuming Coulomb friction between the tangential and normal pressure distributions, the resultant forces and torques can be expressed formally with a nonsmooth dependence on the kinematic variables. In the literature, the exact form of the tangential forces is available for special pressure distributions expressed by transcendent functions; recently, an approximate linear model was introduced. Now, we present a nonlinear extension of the approximation, which can be used effectively to characterise slipping-sticking transitions between the bodies.

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The movement of a disc on a rotating horizontal plane with dry friction

Cited by 4 publications

References 2 publications

On Hopf bifurcation in the problem of motion of a heavy particle on a rotating sphere: the viscous friction case

On Hopf bifurcation in the problem of motion of a heavy particle on a rotating sphere: the viscous friction case

On the Dynamics of a Biped upon a Moving Rough Plane

Harmonic expansion and nonsmooth dynamics in a circular contact region with combined slip-spin motion

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