Abstract:
We consider the dynamics of a rod on the plane in a flow of non-interacting point
particles moving at a fixed speed. When colliding with the rod, the particles are reflected
elastically and then leave the plane of motion of the rod and do not interact with it. A thin
unbending weightless “knitting needle” is fastened to the massive rod. The needle is attached
to an anchor point and can rotate freely about it. The particles do not interact with the needle.
The equations of dynamics are obtained, which are piecewise analytic: the phase space is divided
into four regions where the analytic formulas are different. There are two fixed points of the
system, corresponding to the position of the rod parallel to the flow velocity, with the anchor
point at the front and the back. It is found that the former point is topologically a stable focus,
and the latter is topologically a saddle. A qualitative description of the phase portrait of the
system is obtained.
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