×

The early history of Hamilton-Jacobi dynamics 1834-1837. (English) Zbl 1017.01005

The paper is a presentation, discussion and comparison of four fundamental works: William Rowan Hamilton’s dynamical essays of 1834 and 1835 in the Philosophical Transactions of the Royal Society of London, Carl Gustav Jacobi’s letter of 1836 on the three-body problem addressed to the Paris and Berlin academies of science and Jacobi’s article of 1837 in Crelle’s journal on partial differential equations.

MSC:

01A55 History of mathematics in the 19th century
70-03 History of mechanics of particles and systems
70H20 Hamilton-Jacobi equations in mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] David H. Arnold, 1987 : ”The Mechanique physique of Simeon Denis Poisson: The Evolution and Isolation in France of his Approach to Physical Theory ,” University of Toronto Ph.D. dissertation.
[2] Arnold David H., Archive for History of Exact Sciences 28 pp 243– (1983)
[3] Arnold Vladimir I., Mathematical Methods of Classical Mechanics (1989) · doi:10.1007/978-1-4757-2063-1
[4] Gilbert Bliss, 1946 :Lectures on the Calculus of Variations, Chicago. · Zbl 0036.34401
[5] Bolza Oskar, Transactions of the American Mathematical Society 7 pp 459– (1906)
[6] Arthur Cayley, 1857 : ”Report on the Recent Progress of Theoretical Dynamics ,”Report of the British Association for the Advancement of Science, pp. 1 -42 .
[7] Arthur Cayley, 1862 : ”Report on the Progress of the Solution of Certain Special Problems of Dynamics ,”Report of the British Association for the Advancement of Science, pp. 184 -252Mathematical Papers, pp. 184 -252 .
[8] Cayley Arthur, Arthur Cayley 14 (1889) · JFM 26.0034.03
[9] Conway A. W., The Mathematical Papers of Sir William Rowan Hamilton 2 pp 613– (1940)
[10] Demidov Sergey, Archive for History of Exact Sciences 26 pp 325– (1982)
[11] Dirichlet Peter G.L., Jacobi’s Werke 1 pp 225– (1852)
[12] Rene Dugas, 1955 :A History of Mechanics, Neuchatel, republished by Dover, New York in 1988.
[13] Fraser Craig G., Archive for History of Exact Sciences 28 pp 197– (1983) · Zbl 0526.01017
[14] Fraser Craig G., Geschichte der Analysis pp 449– (1999) · doi:10.1007/978-3-8274-2370-2_12
[15] Gelfand Izrail M., Calculus of Variations (1963)
[16] Goldstein Herbert, Classical Mechanics (1950)
[17] Goldstine Herman H., A History of the Calculus of Variations from the 17th through the 19th Century (1980) · Zbl 0452.49002 · doi:10.1007/978-1-4613-8106-8
[18] Robert P. Graves, 1885 :Life of Sir William Rowan Hamilton, Including Selections from His Poems, Correspondence, and Miscellaneous Writings.
[19] Hamilton William R., Mathematical Papers 2 pp 247– (1834)
[20] Hamilton William R., Mathematical Papers 2 pp 513– (1834)
[21] Hamilton William R., Mathematical Papers 2 pp 95– (1835)
[22] Hamilton William R., The Mathematical Papers of Sir William Rowan Hamilton 2 (1940) · Zbl 0156.24201
[23] Hankins Thomas L., Sir William Rowan Hamilton (1980)
[24] Hawkins Thomas, Archive for History of Exact Sciences 42 pp 187– (1991)
[25] James Ivory, 1831 : ”On the Equilibrium of Fluids, and the Figure of a Homogeneous Planet in a Fluid State ,”Philosophical Transactions, pp. 109 -146 .
[26] James Ivory, 1831 : ”On the Theory of the Elliptic Transcendents ,”Philosophical Transactions, pp. 349 -378 .
[27] James Ivory, 1832 : ”On the Theory of the Perturbation of the Planets ,”Philosophical Transactions, pp. 195 -228 .
[28] Jacobi Carl G. J., Annalen der Physik 33 pp 229– (1834) · doi:10.1002/andp.18341090808
[29] Carl G. J. Jacobi, 1836 : ”Uber ein neues Integral fur den Fall der drei Korper, wenn die Bahn des storenden Planeten kreisformig angenommen und die Masse des gestorten vernachlassigt wird ,” Auszug aus einem Schreiben an die Akademie der Wissenschaften zu Berlin.Monatsbericht, Juli 1836, pp. 59 -60 .
[30] Carl G. J. Jacobi, 1836 : ”Sur le Mouvement d’un Point et sur un Cas particulier du Problem des trois Corps ,” Lettre adressee a l’Academie des Sciences de Paris,Comptes Rendus, t.3, pp. 59-61 =Werke4, pp. 37 -38 .
[31] Jacobi Carl G. J., Journal fur die Reine und Angewandte Mathematik 17 pp 68– (1837)
[32] Jacobi Carl G. J., Journal fur die Reine und Angewandte Mathematik 17 pp 97– (1837)
[33] Carl G. J. Jacobi, and A. Clebsch, 1866 :Vorlesungen uber Dynamik, Berlin, reprinted by Chelsea in 1969.
[34] Jacobi Carl G. J., Karl Weierstrass 8 (1881)
[35] Carl G. J. Jacobi, and Pulte Helmut, 1996 :Vorlesungen uber analytische Mechanik: Berlin 1847/48, Braunschweig/Wiesbaden.
[36] Kargon Robert, Journal for the History of Ideas 26 pp 137– (1965)
[37] Morris Kline, 1972 :Mathematical Thought from Ancient to Modern Times, Oxford. · Zbl 0277.01001
[38] Leo Koenigsberger, 1904 :Carl Gustav Jacob Jacobi, Rede zu der von dem internationalen Mathematiker-Kongress in Heidelberg veranstalteten Feier der hundertsten Wiederkehr seines Geburtstages, gehalten am 9. August 1904. · JFM 35.0011.05
[39] Leo Koenigsberger, 1904 :Carl Gustav Jacob Jacobi, Festschrift zur Feier der hundertsten Wiederkehr seines Geburtstages, Leipzig.
[40] Lagrange Joseph L., OEuvres 1 pp 363– (1762)
[41] Leo Koenigsberger, 1772 : ”Essai sur ie Probleme des trois Corps ,” Prix de l’Academic Royale des Sciences de Paris, tome IX, 1772 =OEuvres6, pp. 229 -331 .
[42] Leo Koenigsberger, 1774 : ”Sur l’Integration des Equations a Differences partielles du premier Ordre ”,Nou-veaux Memoires de l’Academic Royale des Sciences et des Belles-Lettres de Berlin, pp. 353 -372OEuvres, pp. 353 -372 .
[43] Leo Koenigsberger, 1776 : ”Sur les Integrales pariculieres des Equations differentielles ”Nouveaux Memoires de l’Academie Royale des Sciences et des Belles-Lettres de Berlin, pp. 197 -275OEuvres, pp. 197 -275 .
[44] Leo Koenigsberger, 1788 :Mechanique analitique, Paris. Second edition , Mechanique analytique, vol.1 (1788 ) andvol.1 (1788 ), is reproduced in OEuvres =OEuvres11 , 11 .
[45] Leo Koenigsberger, 1797 :Theeorie des Fonctions analytiques, Paris =OEuvres9 .
[46] Leo Koenigsberger, 1806 :Lecons sur le Calcul des Fonctions, Paris =OEuvres10 .
[47] Koenigsberger Leo, OEuvres de Lagrange 14 (1867)
[48] Koenigsberger Leo, The Variational Principles of Mechanics (1970)
[49] Louville Joseph, Journal des Mathematiques pures et appliquees 1 pp 248– (1856)
[50] Lutzen Jesper, Joseph Liouville 1809-1882 (1990) · doi:10.1007/978-1-4612-0989-8
[51] Lutzen Jesper, Archive for History of Exact Sciences 49 pp 1– (1995)
[52] Forest R. Moulton, 1914 :An Introduction to Celestial Mechanics, New York. · JFM 45.1182.06
[53] Nakane Michiyo, Historia Scientiarum 1 pp 27– (1991)
[54] Poincare Henri, Les Methodes Nouvelles de la Mechanique Celeste 1 (1892)
[55] Poisson Simeon D., Journal de l’Ecole Polytechnique 8 pp 266– (1809)
[56] Helmut Pulte, 1989 :Das Prinzip der kleinsten Wirkung und die Kraftkonzeptionen der rationalen Mechanik, Stuttgart. · Zbl 0684.01005
[57] Edward J. Routh, 1898 :A Treatise on Dynamics of a Particle, Cambridge. · Zbl 0063.06603
[58] Scriba Christoph J., Dictionary of Scientific Biography 7 pp 50– (1973)
[59] Thiele Rudiger, Historia Mathematica 24 pp 281– (1997)
[60] Tisserand Francois F., Traite de Mechanique celeste 4 (1896)
[61] Wells Dare A., Schaum’s Outline of Theories and Problems of Lagrangian Dynamics (1967) · Zbl 0189.24203
[62] Edmund T. Whittaker, 1899 : ”Report on the Progress of the Solution of the Problem of Three Bodies ”,Report of the British Association for the Advancement of Science, pp. 121 -159 .
[63] Whittaker Edmund T., A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 4. ed. (1944) · Zbl 0061.41806
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.