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The problem of a balanced dynamically asymmetric ball with a rotor rolling without slipping on an unmoving horizontal absolutely rough plane in a uniform gravity field is considered. Using the methods of computer algebra, we conduct the qualitative analysis of the equations of motion of the body: invariant sets satisfying the necessary conditions for the extremum of the problem’s first integrals are found, and their Lyapunov stability is studied. A mechanical interpretation of the solutions obtained is given.

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On Stationary Motions in the Generalized Problem of the Chaplygin Ball

  • 会议论文

  • 发表日期：

    2026年

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  • Valentin Irtegov,
  • Tatiana Titorenko

摘要

The problem of a balanced dynamically asymmetric ball with a rotor rolling without slipping on an unmoving horizontal absolutely rough plane in a uniform gravity field is considered. Using the methods of computer algebra, we conduct the qualitative analysis of the equations of motion of the body: invariant sets satisfying the necessary conditions for the extremum of the problem’s first integrals are found, and their Lyapunov stability is studied. A mechanical interpretation of the solutions obtained is given.