Vg. Vilke et Mv. Dvornikov, THE ROLLING OF A WHEEL WITH A PNEUMATIC TYRE ON A PLANE, Journal of applied mathematics and mechanics, 62(3), 1998, pp. 359-369
A model of a pneumatic tyre as a system with an infinite number of deg
rees of freedom is proposed, when its surface is represented by the de
formed surface of a torus. Using a number of hypotheses a functional o
f the potential energy of the deformations of the tyre is obtained as
a function of the deformations of its tread. A complete system of equa
tions of motion is obtained, assuming that the wheel rolls without sli
pping in the area of contact of the tread with the plane, with respect
to the previously unknown part of the tread. In two special cases of
the rolling of a wheel with breakaway and on a banking, all the charac
teristics of the motion (the contact area, the tyre deformation, and t
he forces and moments applied to the disc of the wheel) are obtained.
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