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Editorial
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-06-18 , DOI: 10.1002/zamm.202002024


In 1964, Clifford Ambrose Truesdell III [1] published his famous paper on the balance of angular momentum [2]. This paper is remarkable for at least two reasons:

  • The paper of this great American scientist was submitted and published in German.
  • The topic was not new because the balance of angular momentum was established more then two hundred years ago by Euler and others.
The motivation for this paper was the endless discussion on the balances in Continuum Mechanics. The five balances (which are the balances of mass, linear momentum, angular momentum, energy, and entropy (written in form of an inequality) whereby the last two are also known as the first and second law of Thermodynamics) ‐ are presented in different ways [3, 4]. There are ongoing discussions ‐ for example, concerning the second law of thermodynamics. But the focus of Truesdell was on balance of angular momentum.

The reason for that were (maybe) the following two questions:

  • is there the independence of the balance of linear momentum and the balance of the angular momentum; and
  • it is possible to extend the formulation of the balance of angular momentum for n point‐masses with the help of the limit n to the case of a continuum?
Since 1964 several scientists came back to these questions. We mention here only two of many interesting publications [5, 6]. Pavel A. Zhilin [7] was a motivation for the first paper of this issue, the author of [4] will stimulate the further teaching in this field. The first paper of this issue demonstrates new developments in the theory of generalized continua with internal degrees of freedom. They do not contradict Truesdell's paper. However, an extension of the classical balances is necessary with respect to the different modelling scales.

Holm Altenbach & Wolfgang H. Müller



中文翻译:

社论

1964年,克利福德·安布罗斯·特吕斯特(Clifford Ambrose Truesdell III)[ 1 ]发表了他关于角动量平衡的著名论文[ 2 ]。这篇论文之所以出色,至少有两个原因:

  • 这位伟大的美国科学家的论文以德语提交并发表。
  • 这个话题并不是什么新鲜事物,因为角动量平衡是在200年前由Euler等人建立的。
本文的动机是对连续体力学中的平衡进行无休止的讨论。五个平衡(质量,线性动量,角动量,能量和熵的平衡(以不等式形式表示),其中后两个也被称为热力学第一定律和第二定律)以不同的方式表示方式[ 3,4 ]。正在进行中的讨论-例如,关于热力学第二定律。但是Truesdell的重点是角动量的平衡。

其原因是(也许)以下两个问题:

  • 线性动量平衡和角动量平衡之间是否独立;和
  • 借助极限可以扩展n个点质量的角动量平衡公式 ñ 连续的情况?
自1964年以来,几位科学家回到了这些问题。在这里,我们仅提及许多有趣的出版物中的两个[ 5、6 ]。Pavel A. Zhilin [ 7 ]是本期第一篇论文的动机,[ 4 ]的作者将激发该领域的进一步教学。本期第一篇论文展示了具有内部自由度的广义连续性理论的新发展。它们与Truesdell的论文并不矛盾。但是,对于不同的模型比例,经典天平的扩展是必要的。

Holm Altenbach和WolfgangH.Müller

更新日期:2020-06-18
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