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<p>We present some new Poisson bivectors that are invariants by the flow of the nonholonomic Suslov problem.Two rank-four invariant Poisson bivectors have globally defined Casimir functions and, therefore, define cubic Poisson brackets of the five-dimensional state space with standard symplectic leaves. For the Suslov gyrostat in the potential field we found rank-two Poisson bivectors having only two globally defined Casimir functions and, therefore, we say about formal Hamiltonian description in these cases.</p>

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On a Novel Hamiltonian Description of the Nonholonomic Suslov Problem

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • Andrey V. Tsiganov

摘要

We present some new Poisson bivectors that are invariants by the flow of the nonholonomic Suslov problem.Two rank-four invariant Poisson bivectors have globally defined Casimir functions and, therefore, define cubic Poisson brackets of the five-dimensional state space with standard symplectic leaves. For the Suslov gyrostat in the potential field we found rank-two Poisson bivectors having only two globally defined Casimir functions and, therefore, we say about formal Hamiltonian description in these cases.