3 research outputs found
On a mechanical lens
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
Dynamics of a body sliding on a rough plane and supported at three points
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