The present paper is a companion to the paper by Villone and Rampf (2017), titled “Hermann Hankel’s On the general theory of motion of fluids, an essay including an English translation of the complete Preisschrift from 1861” together with connected documents [Eur. Phys. J. H 42, 557–609 (2017)]. Here we give a critical assessment of Hankel’s work, which covers many important aspects of fluid dynamics considered from a Lagrangian-coordinates point of view: variational formulation in the spirit of Hamilton for elastic (barotropic) fluids, transport (we would now say Lie transport) of vorticity, the Lagrangian significance of Clebsch variables, etc. Hankel’s work is also put in the perspective of previous and future work. Hence, the action spans about two centuries: from Lagrange’s 1760–1761 Turin paper on variational approaches to mechanics and fluid mechanics problems to Arnold’s 1966 founding paper on the geometrical/variational formulation of incompressible flow. The 22-year-old Hankel − who was to die 12 years later — emerges as a highly innovative master of mathematical fluid dynamics, fully deserving Riemann’s assessment that his Preisschrift contains “all manner of good things.”

中文翻译：

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赫尔曼·汉克尔（Hermann Hankel）1861年关于拉格朗日流体动力学的开创性工作的当代观察

本论文是Villone和Rampf（2017）发表的论文的同伴，题为“ Hermann Hankel的“关于流体运动的一般理论”，该论文包括1861年以来的完整Preisschrift的英文翻译”以及相关文档[Eur。物理 J·H 42，557–609（2017）]。在这里，我们对汉克尔的工作进行了批判性评估，其中涵盖了从拉格朗日坐标的角度考虑的流体动力学的许多重要方面：汉密尔顿精神中的弹性（正压）流体，运输（我们现在称为李运输） ），旋涡性，克莱布施变量的拉格朗日意义等。汉高的工作也从以前和将来的工作角度出发。因此，这一行动跨越了两个世纪：从拉格朗日（Lagrange）在1760–1761年都灵（Turin）发表的有关力学和流体力学问题的变分方法的论文到阿诺德（Arnold）在1966年发表的关于不可压缩流的几何/变分公式的论文。22岁的汉高（Hankel）即将在12年后去世，他是一位极富创新精神的数学流体动力学大师，Preisschrift包含“各种形式的美好事物”。