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首页> 外文期刊>Journal of Mathematical Sciences >GEOMETRIC AND DYNAMICAL INVARIANTS OF INTEGRABLE HAMILTONIAN AND DISSIPATIVE SYSTEMS
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GEOMETRIC AND DYNAMICAL INVARIANTS OF INTEGRABLE HAMILTONIAN AND DISSIPATIVE SYSTEMS

机译：积分哈密顿系统和耗散系统的几何和动力学不变性

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This paper presents results concerning the geometric invariant theory of completely integrable Hamiltonian systems and also the classification of integrable cases of low-dimensional and high-dimensional rigid body dynamics in a nonconservative force field. The latter problems are described by dynamical systems with variable dissipation. The first part of the work is the basis for the doctorial dissertation of V. V. Trofimov (1953-2003), which was already published in parts. However, in the present complete form, it has not appeared, and we decided to fill in this gap. The second part is a development of the results presented in the doctoral dissertation of M. V. Shamolin and has not appeared in the present variant. These two parts complement one another well, which initiated this work (its sketches already appeared in 1997).
机译：本文介绍了有关完全可积分哈密顿系统的几何不变性理论的结果，以及有关非保守力场中低维和高维刚体动力学的可积分情况的分类。后者的问题由具有可变耗散的动力学系统描述。论文的第一部分是V. V. Trofimov（1953-2003）博士论文的基础，该论文已被部分出版。但是，在目前的完整表格中，它尚未出现，因此我们决定填补这一空白。第二部分是对M. V. Shamolin博士论文提出的结果的发展，并且没有出现在本变体中。这两个部分相互补充，很好地开展了这项工作（其草图已于1997年出现）。

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