Rolling and slipping motion of Euler’s disk
نویسندگان
چکیده
منابع مشابه
The Rolling Motion of a Disk on a Horizontal Plane
Recent interest in the old problem of the motion of a coin spinning on a tabletop has focused on mechanisms of dissipation of energy as the angle α of the coin to the table decreases, while the angular velocity Ω of the point of contact increases. Following a review of the general equations of motion of a thin disk rolling without slipping on a horizontal surface, we present results of simple e...
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The fixed points of the dynamical system describing the rolling motion of a uniform disk or a uniform circular hoop on a rough horizontal plane without dissipation are analyzed. All fixed points of the system are stated to be steady motion states which are either saddle points or centers. The spectral analysis of the sound amplitude time series emitted by a toy of the rolling disk shows that th...
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In the paper we present the qualitative analysis of rolling motion without slipping of a homogeneous round disk on a horisontal plane. The problem was studied by S. A. Chaplygin, P. Appel and D. Korteweg who showed its integrability. The behavior of the point of contact on a plane is investigated and conditions under which its trajectory is finit are obtained. The bifurcation diagrams are const...
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The rolling motion of a rigid cylinder on an inclined flat viscous surface is investigated and the nonlinear resistance force against rolling, FR(v), is derived. For small velocities FR(v) increases with velocity due to increasing deformation rate of the surface material. For larger velocity it decreases with velocity due to decreasing contact area between the rolling cylinder and the deformed ...
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We describe how the dynamical system of rolling two n-dimensional connected, oriented Riemannian manifolds M and M̂ without twisting or slipping, can be lifted to a nonholonomic system of elements in the product of the oriented orthonormal frame bundles belonging to the manifolds. By considering the lifted problem and using properties of the elements in the respective principal Ehresmann connect...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2004
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.69.056610