谢尔盖·阿列克谢耶维奇·恰普雷金Sergey Chaplygin

谢尔盖·阿列克谢耶维奇·恰普雷金的父亲阿列克谢·季莫费耶维奇·恰普雷金是一名店员，在恰普雷金年仅两岁时因霍乱去世，年仅24岁。这意味着他在母亲安娜·彼得罗夫娜的抚养下，在相当贫困的环境中长大。然而，安娜·彼得罗夫娜再婚嫁给了一位来自沃罗涅日的商人，全家离开拉年堡搬到了沃罗涅日。他的母亲热切希望谢尔盖·阿列克谢耶维奇接受教育，因此在他八岁时，她聘请了一位家庭教师，使他的教育达到参加预备班入学考试所需的标准。1877年秋天，他参加了这些考试并开始了学业。

正如我们已经指出的，这家人很穷，所以他们很难支付谢尔盖·阿列克谢耶维奇的学费。然而，他一上学，老师们就清楚地看出他具有非凡的能力和惊人的记忆力。根据老师们的建议，教育委员会决定免除他的学费要求。在沃罗涅日文理中学就读期间，他同学的父母意识到他的非凡才能，请他辅导他们的儿子。因此，他在十四岁时就开始了教学生涯，成为一名受欢迎的私人教师。他从私人辅导中赚的钱帮助养家。他在所有学校科目中都表现出色，在古代语言、现代语言、历史和其他科目上同样优秀。然而，他最喜欢的是数学，他决定以此学科为职业。他于1886年从中学毕业，获得金牌，他的老师A P Kiselev预测：-

……谢尔盖·阿列克谢耶维奇有着伟大的未来。

那年秋天，十七岁的恰普雷金收拾了一个小手提箱，口袋里揣着200卢布，从沃罗涅日出发前往莫斯科，开始他的大学数学学习。

在莫斯科大学，恰普雷金就读于物理数学系，头两年他完全专注于数学课程。然而，从第三年开始，他的兴趣转向专攻力学。他深受尼古拉·叶戈罗维奇·茹科夫斯基的影响，后者就广泛的主题为他授课。1890年恰普雷金获得第一个学位毕业后，尼古拉·叶戈罗维奇·茹科夫斯基说服他继续攻读大学教师资格。他的第一项工作是在尼古拉·叶戈罗维奇·茹科夫斯基的影响下完成的流体动力学研究；特别是关于液体和气体的力学，在1890年代研究射流流动。1893年恰普雷金发表了On certain cases of the motion of a solid body in a fluid，这项工作的质量如此杰出，以至于他因此贡献被授予尼古莱·布拉什曼奖。1897年他提交了硕士学位论文（相当于博士学位），该论文于1893年以同名发表。Grigorian写道[1]：-

恰普雷金对液体中物体运动的那些情形给出了几何解释，这些情形此前曾由德国科学家阿尔弗雷德·克莱布什和古斯塔夫·基尔霍夫以及俄罗斯科学家弗拉基米尔·安德烈耶维奇·斯捷克洛夫从纯分析的角度进行研究。在这方面，尼古拉·叶戈罗维奇·茹科夫斯基写道，恰普雷金“在他的两篇优秀论文中展示了巧妙构思的几何研究方法能够具有何等力量。”

St Petersburg Academy of Sciences因这项杰出工作授予他金质奖章。

恰普雷金于1893年开始在莫斯科任教。他从1896年到1906年在女子中等教育机构教授物理，在莫斯科高等技术学校教授力学，并在莫斯科工程学校任教。他从1894年起在莫斯科大学担任助理教授，1903年晋升为教授。从1901年起，他担任莫斯科女子学院的力学教授，1905年他帮助组织了莫斯科女子高级课程。他从1905年到1918年担任女子高级课程的主任，当时该高级课程成为第二莫斯科国立大学。Keldysh写道[8]：-

“……在他的领导下，高级课程发展成了一所大型高等教育机构，提供所有知识分支的教学。”

他在1918-19年担任这所大学的校长一年，直到莫斯科的两所大学合并。作为恰普雷金非凡记忆力的一个例证，[12]中记载，在他担任校长期间，他能叫出每个学生的名字。

获得硕士学位（相当于博士学位）后，恰普雷金研究了理论力学的两个经典问题。一个是研究受非可积约束的物体的运动，另一个是研究重物体绕固定点的运动。他的论文On the motion of a heavy body of revolution in a horizontal plane（1897年）首次给出了非完整系统的一般运动方程。这个方程是约瑟夫·拉格朗日方程的推广。同年，他发表了On a certain possible generalisation of the theorem of areas。1899年，他被授予圣彼得堡科学院的金质奖章：-

……因他对物体在流体中运动的理论以及具有非可积约束的物体运动的研究。

他在1902年发表了一篇著名论文On gas streams，给出了可压缩气体非连续流动的许多情形的精确解。这篇论文是他提交给莫斯科大学用于获得博士学位（相当于教授资格论文（Habilitation）或理学博士学位）的，为高速空气力学的研究开辟了道路，正如Keldysh所解释的[8]：-

……它给出了一种研究气体在任何亚音速下的射流的方法。当时，对接近音速的气体流动的研究在航空领域没有实际应用。然而，三十年后，恰普雷金的学位论文成为空气动力学专家许多研究的起点，并为解决亚音速流动问题提供了基础。

事实上，恰普雷金是在克里米亚的一个度假胜地度假时写下了他那篇非凡的学位论文。

俄罗斯的政治局势导致莫斯科大学出现问题，对恰普雷金产生了重大后果。该大学成立于1863年，但经过几年学术自由后，其活动受到限制。尽管如此，它继续作为一所优秀大学运作，为恰普雷金提供了非常好的教育。然而，1905-07年第一次俄国革命中，学生们组织成一个寻求推翻沙皇的团体。第一次革命失败后，沙皇对莫斯科大学采取行动，大学多次被关闭。军队驻扎在校园，并对沙皇认为参与反沙皇运动的教授采取行动。1911年，约130名教授因抗议对大学及其教授采取的行动而辞职。恰普雷金是1911年辞职的教授之一，连同他的许多数学同事，如Boleslav Kornelievich Mlodzeevskii（1858-1923），他在莫斯科数学会中非常活跃。

事实上，正是莫斯科数学会在莫斯科数学家们辞去大学职位后的那些年里，对维持他们彼此之间的联系发挥了重要作用。当时尼古拉·叶戈罗维奇·茹科夫斯基是莫斯科数学会的主席，这使恰普雷金更有理由保持高度的参与。恰普雷金向该学会宣读了关于力学和分析中近似方法的论文。他发展了求解微分方程的近似方法，并于1905年向莫斯科数学会提交了关于该主题的首批结果。从1910年起，他研究机翼理论，于当年2月向该学会提交了一篇论文，确定了绕翼型的流动。同年，他在论文On the pressure exerted by a plane-parallel flow on an obstructing body中发表了他的结果，该文给出了翼型上的升力[1]：-

关于确定绕翼环流速率的基本假设首次在这篇论文中被精确陈述。这一假设——即所谓的恰普雷金-尼古拉·叶戈罗维奇·茹科夫斯基假设——给出了流体作用于穿过其中的物体上的力的完整解。这篇文章包含了平面空气动力学的基础，特别是恰普雷金用于计算流体流对阻碍物体所施加压力的著名公式。这些公式被恰普雷金应用于计算各种翼型上的流动压力，并给出了这些翼型的构造。

赫里斯蒂安诺维奇在[9]中关于这项工作写道：-

这项研究最显著的特点是：如果翼型具有圆滑的前缘和尖锐的后缘，那么当它在流体中匀速运动时，会建立起一种环流，并在尖锐后缘处连续泄流。在这种情况下，会产生与攻角成正比的升力。

恰普雷金的重要论文Theory of cascaded airfoils（1914）提出了绕叶栅环流的基本理论，这一理论被用于螺旋桨、涡轮机和其他水力装置的设计。

与尼古拉·叶戈罗维奇·茹科夫斯基一起，恰普雷金计划在莫斯科建立一个航空研究中心。1917年俄国十月革命后，列宁同意建立这样一个中心。中央空气流体动力学研究所，即TsAGI，于1918年成立，恰普雷金从那时起帮助组织该研究所。事实上，从TsAGI成立之时起，他几乎将所有精力都投入到了这个项目中。1921年尼古拉·叶戈罗维奇·茹科夫斯基去世后，恰普雷金成为董事会主席，他担任这一职位直到1930年。他从1928年到1931年担任研究所执行主任，然后成为研究所科学工作的负责人。在他的领导下，TsAGI建成了优秀的实验室，包括1925年的一座风洞。

拉扎尔·阿罗诺维奇·柳斯捷尔尼克于1922年成为莫斯科数学与力学研究所的研究生，在那里他师从恰普雷金。他在[12]中描述了恰普雷金对顶尖学生所持有的极高要求：-

在我学生时代，他常开设关于质点与质点系力学的课程，但即便在这位最杰出学者的讲座上，有时也只有一名学生出席——米纳科夫（后来的力学教授），据说恰普雷金常‘折磨’他，让他解决困难的力学问题。

柳斯捷尔尼克还描述了恰普雷金的外貌：-

恰普雷金有着独特的外貌，仿佛完全由棱角构成。他本可以成为当时流行的立体主义肖像画的理想模特。我认为，某些柔化了这种棱角感的肖像画，反而剥夺了恰普雷金的个性。

然而，20世纪30年代苏联存在政治问题，使得许多顶尖科学家的生活极为艰难。1936年7月3日，莫斯科大学纯粹数学教授尼古拉·卢津成为苏联当局通过报纸Pravda组织的猛烈政治运动的受害者。在文章Enemies under the Mask of a Soviet Citizen中，他被指控进行反苏宣传和破坏活动，理由是他将所有重要成果发表在国外，而在苏联期刊上只发表次要论文。文章声称尼古拉·卢津集以下于一身：-

……道德上的肆无忌惮和科学上的不诚实，以及对苏联生活每一部分的深藏敌意和仇恨。

文章发表一周后，恰普雷金写信给V I 韦尔纳茨基，解释他对同事遭受攻击的感受：-

关于尼古拉·卢津的文章完全令人愤慨：假设他犯了误判某位科学学位或职称申请人的过错，但怎么可能由此跳到蓄意破坏的结论？！……至于文章中随处可见的指控，说法西斯主义以及他拉拢旧的反动莫斯科数学学派，我完全无法理解这些。剩下的是对尼古拉·卢津贡献的批判性评价。但在这方面我必须只说，这暴露了作者们的完全无能，证明他们对他的著作只有微不足道和肤浅的了解，以及他们故意歪曲正确的评价。他的权威与被他与之对比的亚历山大·欣钦的权威不可同日而语。但应该马上做什么？我们怎样才能帮助N. N.？到目前为止我只做了一件事：我给N. N.发了一封电报，副本附上：“对报纸上对您绝对不应有的攻击感到震惊。您享誉世界的高度科学权威不可能被动摇。我确信您会找到内在的力量，冷静面对对您贡献的这种无权威性的批评。我避免提及另一类完全毫无根据的指控。”

恰普雷金因其杰出贡献获得了许多奖项。他于1924年12月6日当选为苏联科学院通讯院士，四年后，于1929年1月12日成为正式院士。同样在1929年，他获得了功勋科学家称号。他于1925年被授予尼古拉·叶戈罗维奇·茹科夫斯基奖。他获得了两枚列宁勋章、两枚劳动红旗勋章，并于1941年被授予社会主义劳动英雄称号。作为恰普雷金思维方式的一个例证，我们引用Lyusternik [12]讲述的一个故事：-

有一天，Sergei Alekseevich从某个旧文件袋中抽出一份手稿，其中包含边界层理论的基础，其发展程度已达到路德维希·普朗特的工作水平。但恰普雷金没有发表这篇论文，因为这个理论没有数学基础。

尽管第二次世界大战于1939年9月以德国和俄罗斯入侵波兰开始，但这对莫斯科的中央空气流体动力学研究所或其工作人员影响甚微。然而，1941年6月22日，德国军队入侵了他们以前的盟友，迅速向东推进进入苏联领土。他们沿着从波罗的海到黑海的广阔战线推进，1941年秋，中央空气流体动力学研究所从莫斯科疏散到喀山和新西伯利亚。恰普雷金负责该研究所的新西伯利亚分所，并迅速组织建造了风洞和研究实验室。然而，艰苦的工作和困难的环境影响了他的健康，他于1942年10月因脑出血去世。

恰普雷金去世后，他又获得了更多荣誉。1942年，USSR Academy of Sciences设立了S A 恰普雷金奖：-

授予力学领域理论研究的最佳原创工作。

他出生的城镇拉嫩堡于1948年更名为恰普雷金。他的论文集于1948至1950年分四卷出版：第1卷，理论力学与数学；第2卷，流体力学与空气动力学；第3卷，关于数学与力学的演讲与报告；第4卷，理论力学讲义。他关于力学与数学的众多论文的选集于1954年和1976年重新出版。月球上的一座环形山以恰普雷金命名。

最后让我们提到，恰普雷金喜欢下国际象棋，并在员工俱乐部与朋友对弈许多小时。

Sergei Alekseevich Chaplygin's father, Aleksei Timofeevich Chaplygin, was a shop assistant who died of cholera at the age of 24 when Chaplygin was only two years of age. This meant that he was brought up in somewhat poor circumstances by his mother Anna Petrovna. However, Anna Petrovna remarried a tradesman from Voronezh and the family left Ranenburg and moved to Voronezh. His mother was keen for Sergei Alekseevich to have an education so, when he was eight years old, she hired a tutor to bring his education up to the standard required for taking the entrance examinations to the preparatory classes. In the autumn of 1877 he took these examinations and began his schooling.

As we have indicated, the family were poor so they would have had great difficulty paying Sergei Alekseevich's school fees. However, as soon as he began his schooling it became clear to his teachers that he had exceptional abilities and a remarkable memory. On his teachers' recommendation the Pedagogical Board decided to waive the fee requirement in his case. While attending Voronezh Gymnasium, the parents of his fellow pupils, realising his extraordinary skills, asked him to tutor their sons. He therefore began his teaching career at the early age of fourteen, becoming a popular private tutor. The money he made from private tutoring helped to support his family. He excelled across the whole range of school subjects, being equally good at ancient languages, modern languages, history, and his other subjects. However, it was mathematics that he enjoyed most and he decided that he wanted to make a career with this subject. He graduated from the Gymnasium in 1886 with the gold medal and a prediction by his teacher A P Kiselev that:-

... Sergei Alekseevich has a great future.

In the autumn of that year, at age seventeen, Chaplygin packed a small suitcase and, with 200 rubles in his pocket, set off from Voronezh to Moscow to begin his university studies of mathematics.

At the University of Moscow Chaplygin studied in the Physics and Mathematics Faculty and, for the first two years, he concentrated exclusively on mathematics courses. However, beginning in his third year his interests moved towards specialising in mechanics. He was strongly influenced by Nikolai Egorovich Zhukovsky who lectured to him on a wide range of topics. After Chaplygin graduated with his first degree in 1890, Zhukovsky persuaded him to continue to study for his university teacher's qualification. His first work was on hydrodynamics, done under Zhukovsky's influence; in particular on the mechanics of liquids and gases, studying jet stream flow in the 1890s. In 1893 Chaplygin published On certain cases of the motion of a solid body in a fluid and the quality of this work was so outstanding that he was awarded the N D Brashman Prize for this contribution. In 1897 he submitted his master's thesis (equivalent to a Ph.D.) which was published under the same title in 1893. Grigorian writes that [1]:-

Chaplygin gave a geometric interpretation of those cases of the movement of a body in a liquid that had earlier been studied from a purely analytic standpoint by the German scientists Clebsch and Kirchhoff, as well as by the Russian scientist Steklov. In this regard Zhukovsky has written that Chaplygin "demonstrated in his two excellent papers what strength the cleverly conceived geometrical methods of investigation can possess."

The St Petersburg Academy of Sciences awarded him their Gold Medal for this outstanding work.

Chaplygin had begun teaching in Moscow in the year 1893. He taught physics at the Women's Secondary Educational Institution and mechanics at the Moscow Higher Technical School from 1896 until 1906, and at the Moscow Engineering School. He taught from 1894 at Moscow University as an assistant professor, being promoted to professor in 1903. From 1901 he was professor of mechanics at Moscow Women's College and in 1905 he helped organise the Moscow Advanced Course for Women. He served as director of the Advanced Course for Women from 1905 to 1918 when the Advanced Course became the Second Moscow State University. Keldysh writes that [8]:-

... under his leadership the advanced courses developed into a large higher educational institution offering instruction in all branches of knowledge.

He became rector of this university for one year 1918-19 until the two universities of Moscow were merged. As an indication of Chaplygin's remarkable memory, it is recorded in [12] that during his time as rector he knew every student by name.

After the award of his Master's Degree (equivalent to a Ph.D.), Chaplygin worked on two classic problems of theoretical mechanics. One of these was the study of the motion of a body subjected to nonintegrable constraints while the other was the study of the motion of a heavy body about a fixed point. His paper On the motion of a heavy body of revolution in a horizontal plane (1897) was the first to present the general equation of motion of a nonholonomic system. This equation is a generalisation of Lagrange's equation. In the same year he published On a certain possible generalisation of the theorem of areas. In 1899 he was awarded the Gold Medal of the St Petersburg Academy of Sciences:-

... for his studies of the theory of the motion of a body in a fluid and the motion of bodies with nonintegrable constraints.

He published a famous paper On gas streams in 1902 giving exact solutions to many cases of noncontinuous flow of a compressible gas. This paper, which he submitted to Moscow University for his doctorate (equivalent to the habilitation or D.Sc.), opened the way for a study of high velocity aeromechanics as Keldysh explains [8]:-

... it gave a method of studying jet flows of a gas at any subsonic speed. At that time the investigation of gas flows at speeds near the speed of sound had no practical application in aviation. Three decades later, however, Chaplygin's dissertation served as a starting point for many studies by aerodynamics specialists and provided the basis for the solution of problems of subsonic flows.

In fact Chaplygin wrote his remarkable dissertation while he was on vacation at a resort in the Crimea.

The political situation in Russia led to problems in Moscow University that had major consequences for Chaplygin. The University had been founded in 1863 but after a few years of academic freedom, it was restricted in its activities. Nevertheless it continued to operate as an excellent university, providing Chaplygin with a very good education. However, the first Russian Revolution of 1905-07 saw the students organise themselves into a group seeking the overthrow of the tsar. After this First revolution failed, the tsar took action against Moscow University and it was closed on a number of occasions. Troops were stationed on the campus and action was taken against professors whom the tsar thought had been behind the anti-tsarist movement. In 1911 around 130 professors resigned in protest at the actions that were being taken against the university and its professors. Chaplygin was one of the professors who resigned in 1911 along with a number of his colleagues in mathematics such as Boleslav Kornelievich Mlodzeevskii (1858-1923), who was very active in the Moscow Mathematical Society.

In fact it was the Moscow Mathematical Society which played an important role in keeping Moscow mathematicians in contact with each other during the years after they resigned their university positions. Zhukovsky was the president of the Moscow Mathematical Society at this time which gave Chaplygin more reason to maintain a high level of involvement. Chaplygin read papers on mechanics and on approximate methods in analysis to the Society. He had developed methods of approximation for solving differential equation and he presented his first results on that topic to the Moscow Mathematical Society in 1905. From 1910 he studied the theory of the aeroplane wing, presenting a paper to the Society in February of that year which determined the flow around a wing section. In the same year he published his results in the paper On the pressure exerted by a plane-parallel flow on an obstructing body, which gave the lift on a wing section [1]:-

The postulate concerning the determination of the rate of circulation around a wing was first precisely stated in this paper. This postulate - the so-called Chaplygin-Zhukovsky postulate - gives a complete solution to the problem of the forces exerted by a stream on a body passing through it. This article includes the fundamentals of plane aerodynamics, particularly Chaplygin's celebrated formulas for calculating the pressures exerted by the stream of a fluid on an impeding body. These formulas were applied by Chaplygin to the calculation of the stream pressure on various wing profiles for which he gives the construction.

Khristianovich writes about this work in [9]:-

The most notable feature of this study is the statement that if the wing profile has a rounded leading edge and a sharp trailing edge then as it moves uniformly in a fluid, a circulatory flow is established with continuously shedding flow at the sharp trailing edge. In this case a lift proportional to the angle of attack develops.

Chaplygin's important paper Theory of cascaded airfoils (1914) presented the basic theory of circulation round cascades, the theory which is used in the design of propellers, turbines and other hydraulic devices.

Together with Zhukovsky, Chaplygin planned for the setting up of an aeronautical research centre in Moscow. Following the Russian October Revolution of 1917, Lenin agreed that such a centre should be set up. The Central Aerohydrodynamic Institute, or TsAGI, was founded in 1918 and Chaplygin helped organise the Institute from that time. In fact from the time that TsAGI was founded, he devoted almost all his energies to the project. On the death of Zhukovsky in 1921, Chaplygin became Chairman of the Board, a position he held until 1930. He was Executive Director of the Institute from 1928 to 1931, then he became head of the scientific work of the Institute. Under his leadership excellent laboratories were built at TsAGI, including a wind tunnel in 1925.

Lazar Aronovich Lyusternik became a research student in the Moscow Institute of Mathematics and Mechanics in 1922 where he was taught by Chaplygin. He describes in [12] the extremely high standards that Chaplygin had for the top students:-

In my student days, he used to give courses on the mechanics of a particle and of a system, but even at the lectures of this most distinguished scholar there was sometimes only one student present - Minakov (later professor of mechanics), whom Chaplygin used to 'torture', so the story goes, by making him solve difficult mechanics problems.

Lyusternik also describes Chaplygin's appearance:-

Chaplygin had a distinctive appearance, as if he was made up entirely of angles. He would have been a good model for the then fashionable cubist portraits. I think some portraits that soften this angularity deprive Chaplygin of his individuality.

However, there were political problems in the Soviet Union during the 1930s which made the life of many top scientists extremely difficult. On 3 July 1936, Nikolai Nikolaevich Luzin, Professor of Pure Mathematics at Moscow University, was the victim of a violent political campaign organized by the Soviet authorities through the newspaper Pravda. In the article Enemies under the Mask of a Soviet Citizen he was accused of anti-Soviet propaganda and sabotage by publishing all his important results abroad and only minor papers in Soviet journals. The article claimed that Luzin combined:-

... moral unscrupulousness and scientific dishonesty with deeply concealed enmity and hatred to every bit of the Soviet life.

A week after the article appeared, Chaplygin wrote to V I Vernadsky explaining how he felt at the attack on his colleague:-

The article about Luzin is completely outrageous: Supposing that he committed the sin of misjudging some applicant for a scientific degree or title, but how is it possible to jump to the conclusion of sabotage from that?! ... As far as the accusations, slipped in throughout the article, of fascism and his enlisting the old reactionary Moscow school of mathematics, I am complete unable to understand these. There remains the critical evaluation of Luzin's contributions. But in this regard I must say only that this discloses the complete incompetence of the authors which proves their minor and superficial acquaintance with his works and their deliberate distortion of correct evaluation. His authority is incomparable with that of Khinchin who is counterpoised to him. But what should be done right away? How can we help N. N.? I did only one thing so far: I sent N. N. a cable whose copy I attach: "Dumbfounded by absolutely undeserved newspaper attacks against you. Your high world-wide acknowledged scientific authority cannot be shaken. I hope definitely that you will find the inner forces to face this inauthoritative criticism of your contributions calmly. I avoid mentioning the completely groundless accusations of the other sort."

Chaplygin received many awards for his outstanding contributions. He was elected a corresponding member of the USSR Academy of Sciences on 6 December 1924 then, four years later, he became a full member on 12 January 1929. Also in 1929 he received the title of Honoured Scientist. He was awarded the N E Zhukovsky Prize in 1925. He received two Orders of Lenin, two Orders of the Red Banner of Labour, and was awarded the title Hero of Socialist Labour in 1941. As an indication of Chaplygin's way of thinking, we quote a story told by Lyusternik [12]:-

One day Sergei Alekseevich pulled from some bag of old papers a manuscript containing the foundations of a theory of the boundary layer, developed as far as Prandtl's work. But Chaplygin had not published this paper, since this theory did not have a mathematical basis.

Although World War II started in September 1939 with the German and Russian invasion of Poland, this had little effect on the Central Aerohydrodynamic Institute in Moscow or on its staff. However, on 22 June 1941 the German armies invaded their former ally pushing rapidly east into Soviet lands. They advanced along a broad front from the Baltic to the Black Sea and, in the autumn of 1941, the Central Aerohydrodynamic Institute was evacuated from Moscow to Kazan and Novosibirsk. Chaplygin took charge of the Novosibirsk branch of the Institute and rapidly organised the building of a wind tunnel and research laboratories. However, the hard work and difficult circumstances told on his health and he died from a brain haemorrhage in October 1942.

Further honours were given to Chaplygin following his death. In 1942 the USSR Academy of Sciences established the S A Chaplygin Prize:-

For the best original work in theoretical research in the field of mechanics.

Ranenburg, the town of his birth, was renamed Chaplygin in 1948. His collected papers were published in 1948-1950 in four volumes: Volume 1. Theoretical mechanics and mathematics; Volume 2. Hydromechanics and aerodynamics; Volume 3. Lectures and presentations on mathematics and mechanics; and Volume 4. Lecture courses on theoretical mechanics. Selections of his many papers on mechanics and mathematics were re-published in 1954 and 1976. A crater on the moon has been named for Chaplygin.

Finally let us mention that Chaplygin loved playing chess and spent many hours playing against friends in the staff club.