A Hamiltonian and action principle formalism for deriving three-dimensional gyroviscous magnetohydrodynamic models is presented. The uniqueness of the approach in constructing the gyroviscous tensor from first principles and its ability to explain the origin of the gyromap and the gyroviscous terms are highlighted. The procedure allows for the specification of free functions, which can be used to generate a wide range of gyroviscous models. Through the process of reduction, the noncanonical Hamiltonian bracket is obtained and briefly analysed.

中文翻译：

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一类三维陀螺粘性磁流体动力学模型

提出了一种用于推导三维陀螺粘性磁流体动力学模型的哈密顿量和作用原理形式。强调了从第一原理构造陀螺粘性张量的方法的独特性以及它解释陀螺图和陀螺粘性项起源的能力。该过程允许指定自由函数，可用于生成范围广泛的陀螺粘性模型。通过约简的过程，得到了非规范哈密顿括号并进行了简要分析。