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<p>We study the dynamics of a homogeneous rod on a plane, hinged at one of its points and freely rotating about it, in a flow of noninteracting point particles moving with constant velocity and colliding with the rod according to the billiard law, with at most one impact per particle. We derive the dynamic equations of the rod, analyze local phase portraits near the equilibrium points of the system of equations of motion, and provide a qualitative description of the global phase portrait of the system. It is shown that, up to a homeomorphism, the phase portrait of the system coincides with that of a mathematical pendulum with friction when the rod is mounted asymmetrically. Bibliography&#xa0;:&#xa0; 12 titles. Illustrations&#xa0;:&#xa0; 6 figures.</p>

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DYNAMICS OF AN ASYMMETRIC VANE IN A RAREFIED FLOW

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • N. R. Ziatdinov

摘要

We study the dynamics of a homogeneous rod on a plane, hinged at one of its points and freely rotating about it, in a flow of noninteracting point particles moving with constant velocity and colliding with the rod according to the billiard law, with at most one impact per particle. We derive the dynamic equations of the rod, analyze local phase portraits near the equilibrium points of the system of equations of motion, and provide a qualitative description of the global phase portrait of the system. It is shown that, up to a homeomorphism, the phase portrait of the system coincides with that of a mathematical pendulum with friction when the rod is mounted asymmetrically. Bibliography :  12 titles. Illustrations :  6 figures.