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"纳维-斯托克斯方程"还是“纳维-圣维南方程”?圣维南为何缺位?

已有 5445 次阅读 2015-10-30 14:17 |个人分类:社会观察|系统分类:观点评述

                                 ——巴黎综合工科学校教授傅利叶:纳维的恩师与终身的朋友

                               ——巴黎综合工科学校毕业,深造去哪儿?纳维:桥梁公路学校

                               ——巴黎综合工科学校毕业,深造去哪儿?柯西:桥梁公路学校

                             —— 厌战反战让圣维南名誉大损:名校学子失学9年后始得转学!

                             ——巴黎综合工科学校除名,转学去哪儿?圣维南:桥梁公路学校

                             ——被巴黎综合工科学校除名,圣维南的反战思想与纳维也许有关

                               ——工作去哪儿?纳维与圣维南不约而同:法国桥梁公路学校!

                                      ——纳维与圣维南在桥梁公路学校先是师生,后皆从教

                                      ——纳维与圣维南政治观点相近,均持强烈的反战立场

                                       ——圣维南为恩师纳维尔原著作注,注解占全书9/10

                                           ——圣维南是力学名家布辛涅斯克的恩师与伯乐

                                     ——法国为何将师生联手殊荣拆分奉送给英国的斯托克斯

                                       —— 流体力学基石之NS方程:但知有斯,不知有圣?

                                       ——研究表明,NS方程被不同研究者先后独立发现5次

       "纳维-斯托克斯方程"是流体力学中非常有名的方程。武际可老师在《1920年以前力学发展史上的100篇重要文献》(http://blog.sciencenet.cn/blog-39472-225736.html)名下列出了纳维与斯托克斯的重要文献,未提及圣维南(Saint-Venant)1843年发表的《流体动力学研究》。

       百度百科"纳维-斯托克斯方程"词条(http://baike.baidu.com/link?url=EqoTMNkjBesBR3pMTvMSqKj12kAlFiZReEV6kV99aINs48GQrjO3dxhEpbg82m5gkOmmJ_TMJYaHQQTT-i-07)尽管同时提到了纳维、斯托克斯与圣维南(纳维-斯托克斯方程(英文名;Navier-Stokes equations),描述粘性不可压缩流体动量守恒的运动方程。简称N-S方程。粘性流体的运动方程首先由Navier在1827年提出,只考虑了不可压缩流体的流动。Poisson在1831年提出可压缩流体的运动方程。Saint-Venant在1845年,Stokes在1845年独立提出粘性系数为一常数的形式,现在都称为Navier-Stokes方程,简称N-S方程。)不过,还是犯了一个明显的史实错误,将其他正式文献已指出的“早于斯托克斯两年公开发表成果的圣维南(1843)”与斯托克斯的发表时间都称作1845年。

       2002年发表的一篇英文论文(作者:Olivier Darrigol等。转引自百度文库PDF文件,翻译者:刘志海,ledzepplin95@yahoo.com.cn),名称为《在水动力学和弹性力学之间:NS方程起初的五次诞生》(Arch. Hist. Exact Sci. 56(2002) 95-150. © Springer-Verlag 2002),回顾了纳维-斯托克斯方程的发现过程:“无论NS方程解的特征是多么复杂和不可预测,现在一般都以其作为流体力学的普遍基础。众所周知它也是唯一的与应力应变关系的各向同性和线性协调的水动力学方程。不过它的早期正如浪尖上的泡沫一样短暂。最初1822年Navier的证明并没有影响力。方程被重新发现或者推导了至少四次,1823年Cauchy,1829年Poisson,1837年Saint-Venant,1845年Stokes。每个新的发现者或忽视或毁坏了前辈的贡献。大家各行其是推得方程。每个人对方程所应用的系统的运动类型和本质下了不同的断言。...NS 方程的五位发现者都认为分子存在,但是他们在各自的推导本质上在什么程度上与分子假设相关分歧相当大。这些方法的差异很大程度上解释了为何Navier 的后继者忽视或者批评他的NS 方程的推导。他由分子级转到宏观级的捷径看起来任意甚至说是自相矛盾。Cauchy和Poisson简直忽视了Navier对流体动力学的贡献。Saint-Venant和Stokes都把方程归功于Navier,但是认为替代的推导是必要的。直到今天,Navier的贡献还经常被轻视,虽然经过仔细的验证他的方法证明比肤浅读物暗示的远为一致。在流体力学以及弹性理论中的众多方法论态度都是由数学严密性的不同观点以及与工程问题关联的不同程度而推得。Cauchy和Poisson,都最少地涉及工程而最精通高等数学,肯定怀疑过Navier将物理直觉注入到数学推导中的路数。也有许多工程师认定Navier 解决工程问题的方法有太多的数学过于理想化。分歧由个人抱负和领先顺序的争论得到加强,甚至偶尔由其决定。意识到这些压力,Saint-Venant 发展了一种崭新的策略将数学严格性和实用的要求结合起来。Navier-Stokes方程的许多作者在他们所预想的应用类型也是不同的。Navier和Saint-Venant 想到的是管渠流。Cauchy 和Poisson 的兴趣是哲学性质胜于实用。Cauchy 甚至不想将方程应用于真实流体:他只是为“完全非弹性固体”推得方程,并且注意到在慢速运动的极限情况下其等同于Fourier的热方程。最后,Stokes欣然受到英国测地线测量的激发。此种测量需要钟摆振动的空气动力学修正。让Navier 感到失望的是,他的方程仅对于慢速正常运动表现良好。对于钟摆和毛细管这就足够了,但是对于水力学近乎毫无价值。甚至在正常流动的情况下,应用仍受边界条件的困扰。此边界条件是由以前毛细管的试验推出的,后来又放弃了。在湍流的情形,对于水力工程师的经验方法没有替代品。Saint-Venant不过是重新解释了Navier 的方程,将其推广到包含大尺度平均运动的情形,其有效粘度取决由小尺度不规则运动。”

       据介绍(http://www.bing.com/knows/search?q=%E5%9B%BD%E7%AB%8B%E8%B7%AF%E6%A1%A5%E5%AD%A6%E6%A0%A1&mkt=zh-cn):“法国国立路桥学校,又名巴黎高科路桥学校,坐落于法国巴黎法兰西岛大区。国立路桥学校建校于1747年,是法国历史上第一所综合性研究生工程师学校。1991年该校加入巴黎高科高校联盟并正式更名为巴黎高科路桥学校。她是法国精英教育的杰出代表,是法国社会高级决策者和高级工程师的摇篮,她也是法国最顶尖的工程师学校之一。”

      法国国立路桥学校也常被简单翻译为“桥梁公路学校”,博文为保持有关参考文献原样起见,没有进行统一调整。按照法语原文(école des Ponts et Chaussées)的次序,确实是“桥梁公路学校”。不过,中文语境在“桥梁、道路”并提时,一般简化为“路桥”。

       “桥梁公路学校”当时可能既是第一所、也是仅有的综合性研究生工程师学校。纳维与法国著作数学家和力学家柯西(http://www.baike.com/wiki/%E6%9F%AF%E8%A5%BF%EF%BC%8CA.-L.)在巴黎综合工科学校毕业都去了桥梁公路学校进行深造。另据介绍,法国物理学家贝克勒尔、菲涅耳、科里奥利、皮托及水利学家达西等都是从综合工科学校毕业后进入桥梁公路学校继续深造。  

       英格兰圣安德鲁大学数学与统计学院的网站在圣维南简要介绍(http://www-history.mcs.st-andrews.ac.uk/Biographies/Saint-Venant.html)中写道:“Saint-Venant worked mainly on mechanics, elasticity, hydrostatics and hydrodynamics. Perhaps his most remarkable work was that which he published in 1843 in which he gave the correct derivation of the Navier-Stokes equations. Anderson writes in[2]:-Seven years after Navier's death, Saint-Venant re-derived Navier's equations for a viscous flow, considering the internal viscous stresses, and eschewing completely Navier's molecular approach. That 1843 paper was the first to properly identify the coefficient of viscosity and its role as a multiplying factor for the velocity gradients in the flow. He further identified those products as viscous stresses acting within the fluid because of friction. Saint-Venant got it right and recorded it. Why his name never became associated with those equations is a mystery. certainly it is a miscarriage of technical attribution.We should remark that Stokes, like Saint-Venant, correctly derived the Navier-Stokes equations but he published the results two years after Saint-Venant.”该网站并没有按照力学的主流观点将“弹性力学中的圣维南原理”视为圣维南的最大成就,而是将他1843年推导纳维方程并发表的流体力学论文称为他最杰出的工作(Perhaps his most remarkable work was that which he published in 1843 in which he gave the correct derivation of the Navier-Stokes equations.)([2] J D Anderson, A History of Aerodynamics(Cambridge, 1997).

       圣维南替纳维尔原著《材料力学》(或译为《力学在结构和机械方面的应用》)作注一事,武际可老师的博文《从历史上看科学技术教学中的力学》

http://blog.sciencenet.cn/home.php?mod=space&uid=39472&do=blog&id=386505也进行了介绍:“这所学校(指巴黎综合工科学校)的教学组织对世界上其他国家的教学影响很大,后来其他国家的工业高等学校大都仿照这所学校建立。如维也纳工学院、苏黎世工学院、俄国与美国的某些工业院校,都是按照它的模式建立的,有的则完全按照它的教学大纲教学。把基础课和专业课分开来,是教育思想上的巨大进步。后来法国出现了一大批数学和力学的巨人(如柯西、泊松、纳维等、就是该校第一班的学生)。整个弹性力学和流体力学基础的奠定,可以说主要是在法国学者的推动下完成的。就是这种教育思想重大成功的实证。由于这所学校的成功,出了不少名人。第一期入学400名有11名成为院士。弹性力学、流体力学的建立是与这所学校有关的。著名力学家拉格朗日、哥西、圣维南、泊松等都出自这个学校。巴黎综合工科学校所组织的新型的集中授课,就是近代教材的开始。学校组织出版了一批影响很大的教科书。如泊松著的《力学教程》、普朗尼著的《力学分析讲义》、纳维写的《力学在结构和机械方面的应用》(后来经过圣维南对该书的第三版修订补充使篇幅增加了九倍),等。”

       在巴黎综合工科学校就读期间,纳维与老师傅利叶结成了深厚的友谊并成为终身的朋友(During this first year at the école Polytechnique, Navier was taught analysis by Fourier who had a remarkable influence on the young man. Fourier became a life-long friend of Navier as well as his teacher, and he took an active interest in Navier's career from that time on. In 1804 Navier entered the école des Ponts et Chaussées and graduated as one of the top students in the school two years later. http://www-history.mcs.st-andrews.ac.uk/Biographies/Navier.html)。

        纳维与圣维南的师生关系,根据北京大学工学院力学与工程科学系网站摘录的《中国大百科全书·力学》(中国大百科全书出版社,1985年),里面提到“他1864年为老师Claude-Louis-Marie-Henri Navier的著作 《 力学在结构和机械方面的应用 》 编辑第三版时,在书中加入大量注释和附篇”;根据北大工学院的转引,纳维1819年起在桥梁公路学校讲授应用力学,1830年起任教授。圣维南1893年加入巴黎综合工科学校一年左右,1814 年即因政治原因被巴黎综合工科学校除名,1823 年法政府批准他免试进桥梁公路学校学习,1825 年毕业。1837 年起(圣维南)在桥梁公路学校(母校)任教。可以看出,纳维1819年起已在桥梁公路学校任教,圣维南1823年才进入该校就读,受教于纳维自是必然。

        巴黎综合工科学校时期,纳维与圣维南的关系可以说是本文关注的重点之一。限于检索现状,目前尚未见材料直接提及(也许圣维南在《 力学在结构和机械方面的应用 》(第三版)一书中为纳维所作的短传中会有所体现)。根据http://www-history.mcs.st-andrews.ac.uk/Biographies/Navier.html介绍,影响纳维政治态度的两位关键人物是法国著名社会学家孔德与著名哲学家、经济学家、空想社会主义者圣西门。该网页称:“Comte had been educated at the école Polytechnique, entering in 1814, where he had studied mathematics. Navier appointed him as one of his assistants at the école Polytechnique and this connection was to see Navier become an ardent supporter of the ideas of Comte and Saint-Simon. Navier believed in an industrialised world in which science and technology would solve most of the problems. He also took a stand against war and against the bloodletting of the French Revolution and the military aggression of Napoleon.”由此消息可以推知,纳维彼时不是巴黎综合工科学校专职教员,但在该校兼职。彼时任教该校的纳维与1814年入学的孔德及“1814 年因政治原因被除名”的圣维南之间不无关联。圣维南约9年后得以转校复校与纳维的努力应有一定的联系。圣维南在桥梁道路学校毕业后留校,与纳维先后成为该专职教师。圣维南后来并用心尽力为纳维的著作进行了不遗余力的注解。

        英文维基“圣维南”词条仅明确说明圣维南曾受教于盖.吕萨克(He entered the école Polytechnique, in 1813 at sixteen years old.where he studied under Gay-Lussac(1778–1850). Graduating in 1816 he worked for the next 27 years as an engineer.)根据 英文维基“盖.吕萨克” 词条(https://en.wikipedia.org/wiki/Joseph_Louis_Gay-Lussac),彼时盖.吕萨克主要在巴黎大学任教授(In 1802, he was appointed demonstrator to A. F. Fourcroy at the école Polytechnique, where in (1809) he became professor of chemistry. From 1808 to 1832, he was professor of physics at the Sorbonne, a post which he only resigned for the chair of chemistry at the Jardin des Plantes. )。可能仍然在巴黎综合工科学校兼课。英文维基“圣维南”与“纳维”词条只字未提两人之间的师生之谊。实际上这可能是非常重要的。

        名列武际可老师《1920年以前力学发展史上的100篇重要文献》之一的布森涅斯克(注:即布辛涅斯克)(Valentin Joseph Boussinesq ,1842-1929),在《Worlds of Flow_ A History of Hydrodynamics from the Bernoullis to Prandtl》(2005)中则明确指明是圣维南的忠实弟子(Saint-Venant and his disciple Boussinesq sought to describe hydraulicflow through large-scale averaging and effective viscosity.),书中也称圣维南是布森涅斯克的mentor。纳维尔与圣维南

的师生关系详见附录。布森涅斯克由于违背父亲让他接管小农场的愿望、在没有学费来源的情况下,在家乡附近的蒙彼利埃科学学院(Faculty of Sciences at Montpellier)就读了本科。《Science under Control_ The French Academy of Sciences 1795-1914(1992)》介绍(p.226),Boussinesq差不多是自学成才(He did not have the advantage of belonging to any of the grandes ecoles. He was largely self-taught, owing much of his early education to his uncle, a priest. His thesis of 1867 on the diffusion of heat won him the favourable attention of Saint-Venant, who henceforth acted as his patron. In 1870 Saint-Venant, acting as rapporteur for a memoir by Boussinesq, praised the author for his ' remarkable spirit of invention)。他工作之后及攻读博士学位期间有幸认识了圣维南,圣维南给了他大力的鼓励与支持。

        为什么"纳维-斯托克斯方程"没有提及圣维南,比如称为“纳维-圣维南方程”?英格兰圣安德鲁大学数学与统计学院网站的圣维南短传称:“这仍然是一个秘密”(Why his name never became associated with those equations is a mystery)。因为圣维南的公式推导公开发表明显早于斯托克斯两年。

        我对该秘密作些假想,如果圣维南不是由于拒绝参加战争服务,而在法国名誉遭受重创,出现在武际可老师《1920年以前力学发展史上的100篇重要文献》中的也许就不仅是斯托克斯而是圣维南与斯托克斯两者并列了。

        据《Science under Control:the French Academy of Sciences 1795-1914》(Cambridge University Press, 1992, pp.225-226)一书介绍,圣维南在法国学术地位的认可度上也颇费周折。纳维1824年当选院士,可惜51岁就壮年早逝了。圣维南倒是长寿,活到89岁。他46岁首次申报院士,尽管柯西(该书称,柯西的院士资格是通过皇权任命获得,而不是正常的选举过程)对他偏爱有加,但直到柯西死后才当选,评上院士时已是71岁(Saint-Venant, who at the age of forty-six had a considerable record of important publications, received no more than six votes out of a total of fiftyfour. ... Only in 1868 did the Academy agree to admit Saint-Venant,56 who had by then reached the age of seventy-one!)。该书认为,圣维南与柯西同为天主教徒,本身在申报中就处于劣势,保皇主义者柯西在法国科学院也并无多少支持者。布森涅斯克申报院士也非常艰难,该书将之称为天主教徒选举中遭受歧视。

        顺便指出,对本文的推断“被巴黎综合工科学校除名,圣维南的反战思想与纳维也许有关”,限于现有检索结果,这一点尚没有旁证。

        值得注意的是,尽管当时法国社会主流舆论支持参加战争,但纳维持坚定的反战态度。这与圣维南的观点是比较一致的(http://www-history.mcs.st-andrews.ac.uk/Biographies/Navier.html)。

        北京大学工学院力学与工程科学系在其主页开设了“力学大师”栏目(http://web.mech.pku.edu.cn/subpage.asp?id=60),收录的13位力学大师中纳维与圣维南各占一席。

        “关于NS方程被不同研究者先后独立发现5次”的研究上面已经提及。它来自科技史专业研究者Olivier Darrigol(http://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780195392043.001.0001/oxfordhb-9780195392043-e-2,Olivier Darrigol is a CNRS research director in the SPHERE/Rehseis research team in Paris. He investigates the history of physics, mostly nineteenth and twentieth century, with a strong interest in related philosophical questions. He is the author of several books including From c-numbers to q-numbers: The classical analogy in the history of quantum theory (Berkeley: University of California Press, 1992), Electrodynamics from Ampère to Einstein (Oxford: Oxford University Press, 2000), Worlds of flow: A history of hydrodynamics from the Bernoullis to Prandtl (Oxford: Oxford University Press, 2005), and A history of optics from Greek antiquity to the nineteenth century (Oxford: Oxford University Press, 2012).)。Olivier Darrigol的论文《Between Hydrodynamics and Elasticity Theory: The First Five Births of the Navier-Stokes Equation》专门研究了这个问题,他还在他个人独著《Worlds of Flow: A history of hydrodynamics from the Bernoullis to Prandtl(2009)》中进行了阐述。

附1:http://web.mech.pku.edu.cn/subpage.asp?id=396(北京大学工学院力学与工程科学系网站)

                           纳维(Claude-Louis-Marie-Henri Navier 1785~1836)

     法国力学家、工程师。1785年月10日生于第戎,1836年8月21日卒于巴黎。

    少年时由舅父、工程师E.-M.戈泰(1732~1807)照料。1802年进巴黎综合工科学校求学,1804年毕业后进桥梁公路学校求学,1806年毕业。1819年起在桥梁公路学校讲授应用力学,1830年起任教授。1824年被选为法国科学院院士。
    纳维的科学活动开始于1809年编辑出版戈泰的著作和修订B.F.de贝利多(1698~1761)的《工程科学》一书,从引起他对工程科学基础理论的兴趣。巴黎综合工科学校数学分析的传统教育以及在土木工程方面的实践经验,有利于他的力学研究。纳维的主要贡献是分别为流体力学和弹性力学建立了基本方程。1821年他推广了L. 欧拉的流体运动方程,考虑了分子间的作用力,从而建立了流体平衡和运动的基本方程。方程中只含有一个粘性常数。1845年G. G. 斯托克斯从连续统的模型出发,改进了他的流体力学运动方程,得到两个粘性常数的两个流体运动方程(后称纳维-斯托克斯方程)的指教坐标分量形式。1821年,纳维还从分子模型出发,把每一个分子作为一个力心,导出弹性固体的平衡和运动方程(发表于1827年),这组方程只含有一个弹性常数。有两个弹性常数的各项同性弹性力学基本方程是1823年A.-L.柯西得出的。
     纳维在力学其他方面的成就有:最早(1820)用双重三角级数解简支矩形板的四阶偏微分方程;在工程中引进机械功以衡量机器的效率。他在工程方面改变了单凭经验设计建造吊桥(悬索桥)的传统,在设计中采用了理论计算。
    纳维的科学论文发表在法国各科学期刊上,关于流体力学基本方程的论文载于化学年刊第19卷(1821),关于弹性固体平衡和运动方程的文章载于法国科学院研究报告集第7卷(1827)。
                       摘自《中国大百科全书·力学,中国大百科全书出版社,1985年。

附2:http://web.mech.pku.edu.cn/subpage.asp?id=397

                圣维南(Adhemar Jean Claude Barre de Saint – Venant 1797~1886)

      法国力学家。1797年生于福尔图瓦索,1886年1月6日卒于圣旺。

     圣维南出身于一个农业经济学家的家庭。1813 年进巴黎综合工科学校求学,1814 年因政治原因被除名。1823 年法政府批准他免试进桥梁公路学校学习,1825 年毕业。后从事工程设计工作,业余研究力学理论。1834 年发表两篇力学论文,受到科学界重视。1837年起在桥梁公路学校任教。1868年被选为法国科学院院士。
     圣维南主要研究弹性力学。1855 和1856年用半逆解法分别求解柱体扭转和弯曲问题,求解运用了这样的思想:如果柱体端部两种外加载荷在静力学上是等效的,则端部以外区域内两种情况中应力场的差别甚微。J.V.布森涅斯克于1885年把这个思想加以推广,并称之为圣维南原理:设弹性体的一个小范围内作用有一个平衡力系(即合力和合力矩均为零),则在远离作用区处弹性体内由这平衡力系引起的应力是可以忽略的。圣维南原理长期以来在工程力学中得到广泛应用,但是它在数学上的精确表述和严格证明经过将近一百年的时间,才由R.von米泽斯和E.斯特恩贝格作出。但此证明有局限性,后来有人举出了圣维南原理不适用的实例。1868年以后,圣维南研究延性材料的塑性流动,提出塑性流动的基本假设和基本方程。他把这一课题称为塑性动力学
     在流休力学方面,圣维南在 1843 年发表的 《 流体动力学研究》 中列出粘性不可压缩流体运动基本方程,而 G.G.斯托克斯的同一结果则是 1845 年发表的。圣维南还研究过蒸汽机汽缸小孔的气体流量, 1 839 年他和 L.万策尔给出气体通过小孔速度的计算公式,这是气体力学解决的第一批实际问题之一,但当时未引起广泛注意。这公式在 1855 年由J.L.魏斯巴赫重新获得,并曾以魏斯巴赫公式著称于世。
     圣维南研究结果大多发表于法国科学院学报上。他在 1864 年为老师 C-L.-M.-纳维的著作《力学在结构和机械方面的应用 》 编辑第三版时,在书中加入大量注释和附篇,使纳维的原著只占全书的十分之一;圣维南在这些注释和附篇中表述了自己对材抖力学和弹性力学的许多见解。

                                  摘自《中国大百科全书·力学》,中国大百科全书出版社,1985年

附2注:铁木辛科《材料力学史》(中译本)第60页的注解称:“关于纳维埃的传记和他的著作详表可参看圣维南汇编的纳维埃原著‘材料力学’第三版,1864,巴黎”。据此看来,《中国大百科全书·力学》所言的《 力学在结构和机械方面的应用 》可能就是《材料力学》(第三版)。顺便指出,铁木辛科《材料力学史》62页的““1830年,他(注:指纳维埃)成为工业学院的微积分和力学教授”可能有误,似应为“桥梁道路学院(注:铁木辛科原书中译本如此翻译)”。参见附8。又:

http://gc.nuaa.edu.cn/lxjd/lxyd/nw.htm介绍:“纳维(Navier ,claude-Louis-Marie-Henri 1785-1836)于 1807年在桥梁道路学会支持下整理他外祖父的工程建筑的学术手稿。从1819年起,他在桥梁道路学院讲授应用力学,但到1830年才正式被聘任。到1830年,他到巴黎综合工科学校去替柯西任微积分和力学教授。”根据附8等,纳维作教多年后,于1830年被桥梁公路学校聘为教授。

附3:http://gc.nuaa.edu.cn/lxjd/lxyd/svn.htm  

                                                            圣维南及其在弹性力学中的贡献

   圣维南(Saint-Venant,Adhemar Jean Claude Barre.1797—1886)的父亲是一位颇有名气的农村经济学家,在他的细心教导下,圣维南从小就爱好数学,并表现出突出的才能。圣维南稍长,就到布鲁日公立学校上学,1813年他16岁时通过选拔考试进入巴黎综合工科学校。在该校他表现出卓越的才能, 学习成绩名列全班第一名。然而一场政治动乱对他的一生产生了巨大影响。1814年反法联盟军队逼近巴黎,学校动员学生为巴黎的防御工事运送武器,圣维南拒绝参加,被学校除名。此后8年,他一直在火药工厂工作。1823年法国政府批准他免试进人桥梁道路学院,两年后他以全班第一名的成绩毕业。

   1825-1830年,他先后在尼韦奈运河和阿登运河上从事工程设计工作。其间,他利用业余时间研究力学理论。1834年,他向法国科学院提交了两篇关于理论力学和流体力学的论文,并因此在科学界出了名。

   1837年,桥梁道路学院请圣维南讲授材料强度理论。当时关于材料力学的最新讲义是圣维南的老师C.纳维(Navier)编写的《力学在结构和机械方面的应用》(1826)该书以纳维在桥梁道路学院讲授应用力学的讲义为基础整理而成。虽然纳维建立了弹性力学的基本方程,但他在讲义中并没涉及它们,仍然采用平面假定求解问题。圣维南则首先试图把弹性理论的最近进展介绍给他的学生,他对固体的分子结构和分子间的作用力的假设进行讨论,并用这一假设解释了应力概念。1864年圣维南对该书修订第三版时,在书中增加了大量的注释,使原书的篇幅增加了九倍。他还讲授了剪应力和剪应变。由此算出主应力。圣维南在教学中提出的一些问题成为他日后进行科研的课题,他的讲义用石印印出,其原稿现在藏于桥梁道路学院的图书馆。

附4:http://www-history.mcs.st-andrews.ac.uk/Biographies/Saint-Venant.html(英格兰圣安德鲁大学数学与统计学院网站)

 Jean Claude Saint-Venant was a student at the école Polytechnique, entering the school in 1813 when he was sixteen years old. He graduated in 1816 and spent the next 27 years as a civil engineer. For the first seven of these 27 years Saint-Venant worked for the Service des Poudres et Salpêtres, then he spent the next twenty years working for the Service des Ponts et Chaussées.

 Saint-Venant attended lectures at the Collège de France and the lecture notes he took in Liouville's 1839-40 class still survive. He taught mathematics at the école des Ponts et Chaussées where he succeeded Coriolis.

 Saint-Venant worked mainly on mechanics, elasticity, hydrostatics and hydrodynamics. Perhaps his most remarkable work was that which he published in 1843 in which he gave the correct derivation of the Navier-Stokes equations. Anderson writes in [2]:-

Seven years after Navier's death, Saint-Venant re-derived Navier's equations for a viscous flow, considering the internal viscous stresses, and eschewing completely Navier's molecular approach. That 1843 paper was the first to properly identify the coefficient of viscosity and its role as a multiplying factor for the velocity gradients in the flow. He further identified those products as viscous stresses acting within the fluid because of friction. Saint-Venant got it right and recorded it. Why his name never became associated with those equations is a mystery. certainly it is a miscarriage of technical attribution.

 We should remark that Stokes, like Saint-Venant, correctly derived the Navier-Stokes equations but he published the results two years after Saint-Venant.

 Saint-Venant developed a vector calculus similar to that of Grassmann which he published in 1845. He then entered into a dispute with Grassmann about which of the two had thought of the ideas first. Grassmann had published his results in 1844, but Saint-Venant claimed (and there is little reason to doubt him) that he had first developed these ideas in 1832. Again it would appear that Saint-Venant was unlucky. Itard writes in [1]:-

Saint-Venant used this vector calculus in his lectures at the Institut Agronomique, which were published in 1851as "Principes de mécanique fondés sur la cinématique". In this book Saint-Venant, a convinced atomist, presented forces as divorced from the metaphysical concept of cause and from the physiological concept of muscular effort, both of which, in his opinion, obscured force as a kinematic concept accessible to the calculus. Although his atomistic conceptions did not prevail, his use of the vector calculus was adopted in the French school system.

 In the 1850s Saint-Venant derived solutions for the torsion of non-circular cylinders. He extended Navier's work on the bending of beams, publishing a full account in 1864. In 1871 he derived the equations for non-steady flow in open channels.

 In 1868 Saint-Venant was elected to succeed Poncelet in the mechanics section of the Académie des Sciences. By this time he was 71 years old, but he continued his research and lived for a further 18 years after this time. At age 86 he translated (with A Flamant) Clebsch's work on elasticity into French and published it as Théorie de l'élasticité des corps solides and Saint-Venant added notes to the text which he wrote himself. Note that Saint-Venant's co-translator A Flamant was a co-author of the obituary notice [3] for Saint-Venant.

附5:https://en.wikipedia.org/wiki/Adh%C3%A9mar_Jean_Claude_Barr%C3%A9_de_Saint-Venant 

   Adhémar Jean Claude Barré de Saint-Venant was a mechanician and mathematician who contributed to early stress analysis and also developed the unsteady open channel flow shallow water equations, also known as the Saint-Venant equations that are a fundamental set of equations used in modern hydraulic engineering. The 1-D Saint Venant Equation is a commonly used simplification of the shallow water equations. Although his surname was Barré de Saint-Venant in non-French mathematical literature he is known simply as Saint-Venant. His name is also associated with Saint-Venant's principle of statically equivalent systems of load, Saint-Venant's theorem and for Saint-Venant's compatibility condition, the integrability conditions for a symmetric tensor field to be a strain.

   In 1843 he published the correct derivation of the Navier–Stokes equations for a viscous flow[2] and was the first to "properly identify the coefficient of viscosity and its role as a multiplying factor for the velocity gradients in the flow". Even though he published before Stokes, the equations do not bear his name.

[2] J D Anderson, A History of Aerodynamics(Cambridge, 1997).

附6:http://www.baike.com/wiki/%E5%9C%A3%E7%BB%B4%E5%8D%97 

   圣维南 Adhémar Jean Claude Barré de Saint-Venant (1797~1886)  
   法国力学家。1797年生于福尔图瓦索,1886年1月6日卒于圣旺。   
   圣维南出身于一个农业经济学家的家庭。1813年进巴黎综合工科学校求学,1814年因政治原因被除名。1823年法政府批准他免试进桥梁公路学校学习,1825年毕业。后从事工程设计工作,业余研究力学理论。1834年发表两篇力学论文,受到科学界重视。1837年起在桥梁公路学校任教。1868年被选为法国科学院院士。

   在流体力学方面,圣维南在1843年发表的《流体动力学研究》中列出粘性不可压缩流体运动基本方程,而G.G.斯托克斯的同一结果则是1845年发表的。圣维南还研究过蒸汽机汽缸小孔的气体流量,1839年他和L.万策尔给出气体通过小孔速度的计算公式;这是气体力学解决的第一批实际问题之一,但当时未引起广泛注意。这公式在1855年由J.L.魏斯巴赫重新获得,并曾以魏斯巴赫公式著称于世。

   圣维南研究结果大多发表于法国科学院学报上。他在1864年为老师C.-L.-M.-H.纳维的著作《力学在结构和机械方面的应用》编辑第三版时,在书中加入大量注释和附篇,使纳维的原著只占全书的十分之一;圣维南在这些注释和附篇中表述了自已对材料力学和弹性力学的许多见解。

附7:http://blog.sciencenet.cn/blog-39472-225736.html

                                                      1920年以前力学发展史上的100篇重要文献

                                                                       武际可

   在力学发展的历史长河中,文献浩如烟海。要在其中选择最重要的100种会有一定困难。为此我们确定以下两条原则:

   第一,时间限定在1920年以前。一方面是一战后这段时间还不够长,成果的重要性还有待进一步的历史考验,另一方面是一战后各国政府介入科学事业,大量的科学成果很难用文献和书来表达。

   第二,范围包括原创成果和教材。其影响比较长远者。

即使是这样。在选择的取舍上仍然是有困难的,可以有不同的方案。更有一些重要成果,找不到原始文献,如风洞的建造、材料试验机的发明等。所以笔者选定的这100项文献也只是从一个方面反映力学学科的发展。

纳维(Navier1785-1836

42.《论弹性体的平衡与运动》(Sur les lois de l’équilibre et du mouvement des corps solidesélastiques),1821年发表在Bull. Soc. Phlomath177-181),法文。最早提出弹性体运动的一般方程。

43*.《流体的运动法则》(Mémoire sur les lois du mouvement des fluides),1822年提交的研究报告,Mémoriesde l’Académie royale des sciences de l’Institut de France1823年刊出(p.389),,法文。最早提出黏性流体的运动方程。

斯托克斯George Gabriel Stokes18191903

54.《流体运动的内摩擦与弹性固体的运动与平衡》(”On the theories of the internal friction of fluid in motion, and of the equilibrium and motion of elastic solids1845年发表在Trans .Camb. Phil. Soc.上(8, pp. 287-305.),英文。以与纳维不同的方法导出了黏性流体的运动方程,后人称为纳维-斯托克斯方程。

附8:http://www-history.mcs.st-andrews.ac.uk/Biographies/Navier.html

Claude-Louis Navier's father was a lawyer who was a member of the National Assembly in Paris during the time of the French Revolution. However Navier's father died in 1793 when Navier was only eight years old. At this time the family were living in Paris but after Navier's father died, his mother returned to her home town of Chalon-sur-Saône and left Navier in Paris to be cared for by her uncle Emiland Gauthey.

Emiland Gauthey was a civil engineer who worked at the Corps des Ponts et Chaussées in Paris. He was considered the leading civil engineer in France and he certainly gave Navier an interest in engineering. Despite encouraging Navier to enter the école Polytechnique, Gauthey seems not to have been that successful in teaching Navier, who may just have been a late developer, for he only just scraped into to école Polytechnique in 1802. However, from almost bottom place on entry, Navier made such progress in his first year at the école Polytechnique that he was one of the top ten students at the end of the year and chosen for special field work in Boulogne in his second year.

During this first year at the école Polytechnique, Navier was taught analysis by Fourier who had a remarkable influence on the young man. Fourier became a life-long friend of Navier as well as his teacher, and he took an active interest in Navier's career from that time on. In 1804 Navier entered the école des Ponts et Chaussées and graduated as one of the top students in the school two years later. It was not long after Navier's graduation that his granduncle Emiland Gauthey died and Navier, who had left Paris to undertake field work, returned to Paris, at the request of the Corps des Ponts et Chaussées, to take on the task of editing Gauthey's works. Anderson writes in [3]:-

Over the next 13 years, Navier became recognised as a scholar of engineering science. He edited the works of his granduncle, which represented the traditional empirical approach to numerous applications in civil engineering. In that process, on the basis of his own research in theoretical mechanics, Navier added a somewhat analytical flavour to the works of Gauthey. That, in combination with textbooks that Navier wrote for practicing engineers, introduced the basic principles of engineering science to a field that previously had been almost completely empirical.

Navier took charge of the applied mechanics courses at the école des Ponts et Chaussées in 1819, being named as professor there in 1830. He did not just carry on the traditional teaching in the school, but rather he changed the syllabus to put much more emphasis on physics and on mathematical analysis. In addition, he replaced Cauchy as professor at the école Polytechnique from 1831. His ideas for teaching were not shared by all, however, and soon after his appointment to the professorship at the école Polytechnique Navier became involved in a dispute with Poisson over the teaching of Fourier's theory of heat.

附9:http://wenku.baidu.com/link?url=z8cM_70Eu8JHnQGRn3nNpb-eZOKTnLV0RtiQEpMCGVrQ1n-6q-Kr4uEFRdeSZ0B1lLy9lz6QcPjj4Fv2blpugOn3VK4-rWtOVzcGkqKB4sm 




附10:http://www.jstor.org/stable/41134138?seq=1#page_scan_tab_contents 



附11:http://www.amazon.cn/Worlds-of-Flow-A-history-of-hydrodynamics-from-the-Bernoullis-to-Prandtl-Darrigol-Olivier/dp/0198568436

 Worlds of Flow_A History of Hydrodynamics from the Bernoullis to Prandtl(2005),p.101

In the early nineteenth century, the rational fluid mechanics of d'Alembert, Euler, and Lagrange remained irrelevant to the mundane problems of pipe flow and ship resistance. Engineers had their own empirical formulas, and mathematicians their own paper theory of perfectly unresisted flow. A similar contrast existed in the case of elasticity: the formulas established by mathematicians for the flexion of prisms were oflittle help in evaluating the limits of rupture in physical constructions. In the 1820s and 1830s, a new breed of French engineer-mathematicians trained at the Ecole Polytechnique, mainly Navier, Cauchy, and Saint-Venant, struggled to fill this gap between theory and practice. As a preliminary step toward a more realistic theory of elasticity, in 1 821 Navier announced the general equations of equilibrium and motion for an (isotropic, one-constant) elastic body. Transposing his reasoning to fluids, he soon obtained a new hydrodynamic equation for viscous flow, namely the Navier-Stokes equation.

   Navier's latter theory received little contemporary attention. TheNavier-Stokes equation was rediscovered or rederived at least four times, by Cauchy in 1823, by Poisson in 1 829, by Saint-Venant in 1837, and by Stokes in 1 845. Each new discoverer either ignored or denigrated his predecessors' contribution. Each had his own way to justify the equation, although they all exploited the analogy between elasticity and viscous flow. Each judged differently the kind of motion and the nature of the system to which it applied. The comparison between the various derivations of this equation-or of the equations of motion of an elastic bodybrings forth important characteristics of mathematical physics in the period 1820-1850.

附12:   Science under Control:the French Academy of Sciences 1795-1914(p.225)


附13:http://blog.lehu.shu.edu.cn/sqdai/A70834.html 

                                                  问题征答:关于Boussinesq,谁能告诉我更多?
布辛涅斯克Joseph Valentin Boussinesq18421929)是一位非同凡响的法国力学家、物理学家和数学家对水动力学、振动力学、光学和热学理论做出过杰出贡献。谷歌上搜索可得23万条之多。但是,迄今为止,我对他的生平事迹、成长历程、学术思想等等知之甚少;对他的学术贡献也了解得不够全面。这里特提出问题征答,希望朋友们告诉我更多有关他的信息。
下面叙述目前我所掌握的关于Boussinesq的情况。
约瑟夫·瓦伦丁·布辛涅斯克于1842年3月13日生于法国Saint-Andre- de-Sangonis,1929年2月19日卒于巴黎。1872年至1886年任里尔大学科学系教授,讲授微积分;1886年至1918年退休前任巴黎科学院的力学教授。
1834年英国拉塞尔(J.S.Russell)实验观察到了孤立波,1844年在英国科学进展协会的会议上报告了他的结果;此后遭到权威学者艾里、斯托克斯等的非议;1871年,Boussinesq第一个提出数学理论,支持Russell实验观察;1876年,瑞利爵士(Lord Rayleigh)也建立了支持Russell实验观察的数学理论,在他的论文末尾,Rayleigh承认了Boussinesq理论提出在先。
1877年,Boussinesq提出了浅水长波近似,建立了著名的Boussinesq方程,此后得到了广泛的应用和推广。
1877年,Boussinesq在他的论文“Théorie de l’écoulement Tourbillant” Mem. Présentés par Divers Savants Acad. Sci. Inst. Fr., Vol. 23, pp. 46-50)中首次提出湍流涡粘度假设,1897年,他出版了Théorie de l' écoulement tourbillonnantet tumultueux des liquides这一著作对湍流和水动力学做出了巨大贡献。经查,湍流(turbulence)这个名词的提出多半应归功于Boussinesq。
此外,Boussinesq还对小密度差分层流中的浮力驱动流提出了著名的Boussinesq近似,在计及浮力的情况下,提出了简捷可靠的理论。他在弹性力学、岩土力学等方面也有卓越贡献。
由于Boussinesq在流体力学的多个领域里都有贡献,至今很多流体力学著作中不能不提及他。例如,仅Boussinesq近似就有三种,分别涉及浅水波、涡粘度和浮力流(现在大多专指关于浮力流中的近似)。
对于他在光学、热学、数学上的贡献,我不大清楚。我迫切希望全方位地了解这位多姿多彩的学者。希望得到大家的帮助。
   本文主要参考资料来自:http://en.wikipedia.org./wiki/Joseph_Valentin_Boussinesq
 
写于2009424日晨

本组的邝华在第一时间找到了一篇关于Boussinesq的详尽介绍,下载了他的照片,一并发给了我。我不能独享,及时地予以公布,可使大家对这位低调的大家有进一步了解。谢谢邝华!

发布者 sqdai  2009/4/24 11:33:30
Boussinesq成为法国科学院院士的经历比较坎坷。1870年由圣维南(Saint-Venant)首次推荐失败,1868,1871,1872(两次),1873,1880以及1883年的申请均告失败。1883年圣维南已经是力学组的头。他在1886年的选举推荐报告被保存了下来,可能想到Boussinesq会重复自己的老路(圣维南由柯西推荐申请院士,到柯西死后才被评上,46岁首次参加,到评上院士时是71岁),他指出Boussinesq是唯一一位应该评上院士的生存者了,这是圣维南为Boussinesq做的最后的努力。圣维南死于1886年1月6号,而选举投票日期是1886年1月18号,Boussinesq以微弱票当选(29票,竞争对手Deprez得到26票)。
选自Maurice Crosland Science under Control:the French Academy of Sciences 1795-1914. Cambridge University Press, 1992, p225-226上海图书馆有此书
发布者 glennzsguo    2009/4/25 2:58:18
引用 sqdai 发表于 2009/4/25 6:17:54 的话:
谢谢glennzsguo!我昨天晚饭后读了邝华推介的文章,觉得Boussinesq遭遇这一挫折的原因是他的独来独往的孤傲性格。多亏圣维南的无私提携!欢迎各位进一步提供新材料,尤其是在里尔的黄永祥。
好像几年前里尔大学有一个纪念会议,Francois有参加的。我明天问问看他有没有那次的会议文集,里面应该有Boussinesq的详细介绍吧,希望别是法语的,呵呵

发布者 黄永祥  2009/4/26 16:29:01

Boussinesq在里尔大学(那时叫里尔理工大学)度过了16年(最富有创造性的年华),他的主要学术贡献几乎都在此时做出的,校园里应有很多遗迹(例如塑像)可寻。请你读读附件中的文章。我对他感兴趣是因为他是流体力学史中不可或缺的人物,却在大英百科全书和我国的大百科全书(力学卷)中没有他的传略,更想了解他。

附14:http://www-history.mcs.st-andrews.ac.uk/Biographies/Boussinesq.html

                                   圣维南对布辛涅斯克的提携与师生谊

                                (陈昌春:标题系我另加)

 He(Boussinesq) began working for a doctorate on A mechanical theory of light supervised by émile Verdet. However, Verdet died in 1866 before Boussinesq's thesis was completed. He was then given another supervisor and, to suit his new supervisor's interests, Boussinesq changed the topic of his thesis and wrote études sur la propagation de la chaleur dans les milieux homogènes (Study of propagation of heat in homogenous media). Lamé had played a major role in advising Boussinesq and the thesis clearly shows his influence in the way Boussinesq approached his subject. Another mathematician who influenced the work was Saint-Venant. The examining committee, however, comprised of Joseph Serret, Joseph Bertrand and Charles Auguste Briot and Boussinesq defended his thesis in Paris before this committee on 13 May 1867.

 Boussinesq had not concentrated on his thesis to the exclusion of other research, for he had worked on the theory of linear elasticity at the same time. This topic was particularly fascinating to Saint-Venant who corresponded regularly with Boussinesq and gave him much encouragement to believe that he had a future as a research mathematician rather than as a school teacher of mathematics [5]:-

 Boussinesq was not a lucid writer and was often too impatient in giving logical explanations so that, on several occasions, Saint-Venant advised him to give clear and detailed arguments in his work.

 In fact from this time on Saint-Venant was Boussinesq's staunchest supporter and became even more influential in 1868 when he was elected to succeed Poncelet in the mechanics section of the Académie des Sciences. Boussinesq had married Jeanne Giscard de la Roque in 1867 and, but for Saint-Venant's support and advice, might well have settled down to teaching in secondary schools. Saint-Venant understood the system well and was able to advise Boussinesq that to obtain a university position in mechanics would be very difficult unless he had both a mathematics and a physics qualification. He followed this advice and in 1872 was awarded a Bachelor's degree in physics. The Académie des Sciences awarded him their Poncelet Prize in 1872 and he was well set up for a university appointment. Indeed he succeeded in the following year when he was appointed Professor of Differential and Integral Calculus at the Faculty of Science in Lille.

附15:材料力学史-铁木辛柯(1961年上海科学技术出版社翻译出版)


附16:https://www.vulcanhammer.org/2012/11/09/taking-the-last-voyage-with-newton-and-pascal/

In spite of his difficulties within France, his reputation outside of her was another matter.  When François Napoleon Moigno wrote his book on statics, he discovered the following:

 He (Moigno) wanted the portion on the statics of elastic bodies to be written by an expert in the theory of elasticity, but every time he asked for the collaboration of an English or a German scientist, he was given the same answer: “You have there, close to you, the authority par excellence, M. de Saint-Venant, consult him, listen to him, follow him.” One of them, M. Ettingshausen, added: “Your Academy of Sciences makes a mistake, a great mistake when it does not open its doors to a mathematician who is so highly placed in the opinion of the most competent judges.” In conclusion Moigno observes: “Fatally belittled in France of which he is the purest mathematical glory, M. de Saint-Venant enjoys a reputation in foreign countries which we dare to call grandiose.”

 The French finally broke down and admitted Saint-Venant into the Academy of Sciences in 1868.  He continued his work, much of it from his home, up until the time of his death.  When the President of the Academy announced that passing, he made the following statement:

 Old age was kind to our great colleague.  He died, advanced in years, without infirmities, occupied up to the last hour with problems which were dear to him and supported in the great passage by the hopes which had supported Pascal and Newton.

 Europeans of the time would not have missed the import of the last statement: Pascal and Newton were Christians, and Saint-Venant was being identified with them as one also.  It was also a statement that Saint-Venant, for all of his achievements and interests which have enriched the world, also had an eternal goal as well.

 There’s no evidence that Saint-Venant was ostentatious in his faith walk; descriptions of his life show the contrary.  And–shock to today’s atheist–there’s no evidence that it ever impeded the progress of his research or his thought.  As the statistician and eugenicist Karl Pearson, no friend of Christianity, noted:

 The more I studied Saint-Venant’s work, the more new directions it seemed to me to open up for original investigation of the most valuable kind. It suggested innumerable unsolved problems in atomic physics, in impact, in plasticity and in a variety of other branches of elasticity, which do not seem beyond solution, and the solution of which if obtained would be of extreme importance. I felt convinced that a study of Saint-Venant’s researches would be a most valuable directive to the several young scientists, whose recent memoirs shew their interest in elasticity as well as their mathematical capacity. Many of the problems raised by Saint-Venant’s suggestive memoirs were quite beyond my powers of analysis, and I recognised that the most useful task I could undertake, was by a careful account of the memoirs themselves to lead the more competent on to their solution.

Note: my main source for this article was S. Timoshenko’s History of Strength of Materials.  Other sources were as follows:

  • Pearson, Karl. The Elastical Researches of Barré de Saint-Venant. Cambridge: University Press, 1889.

  • Thurston, Herbert. “Saint Bénézet and his Biographer.” Catholic World, Vol. 86, No. 517, December 1907.

附17:http://blog.sciencenet.cn/blog-44346-24271.html

  George Gabriel Stokes 1819 - 1903:  An Irish Mathematical Physicist

                 Author:Prof Alastair Wood, Dublin City University, Ireland; 1998

 His early research was in the area of hydrodynamics, both experimental and theoretical, during which he(注:Stokes)put forward the concept of "internal friction" of an incompressible fluid. This work was independent of the work of Navier, Poisson and Saint-Venant which was appearing in the French literature at the same time, but Stokes' methods could also be applied to other continuous media such as elastic solids. He then turned his attention to oscillatory waves in water, producing the subsequently verified conjecture on the wave of greatest height, which now bears his name.



http://blog.sciencenet.cn/blog-350729-932151.html

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