Article ID: CBB563006808

Canonical transformations from Jacobi to Whittaker (2023)

unapi

The idea of a canonical transformation emerged in 1837 in the course of Carl Jacobi's researches in analytical dynamics. To understand Jacobi's moment of discovery it is necessary to examine some background, especially the work of Joseph Lagrange and Siméon Poisson on the variation of arbitrary constants as well as some of the dynamical discoveries of William Rowan Hamilton. Significant figures following Jacobi in the middle of the century were Adolphe Desboves and William Donkin, while the delayed posthumous publication in 1866 of Jacobi's full dynamical corpus was a critical event. François Tisserand's doctoral dissertation of 1868 was devoted primarily to lunar and planetary theory but placed Hamilton–Jacobi mathematical methods at the forefront of the investigation. Henri Poincaré's writings on celestial mechanics in the period 1890–1910 succeeded in making canonical transformations a fundamental part of the dynamical theory. Poincaré offered a mathematical vision of the subject that differed from Jacobi's and would become influential in subsequent research. Two prominent researchers around 1900 were Carl Charlier and Edmund Whittaker, and their books included chapters devoted explicitly to transformation theory. In the first three decades of the twentieth century Hamilton–Jacobi theory in general and canonical transformations in particular would be embraced by a range of researchers in astronomy, physics and mathematics.

...More
Citation URI
https://data.isiscb.org/isis/citation/CBB563006808/

Similar Citations

Article Coutinho, S. C.; (2014)
Whittaker's Analytical Dynamics: A Biography (/isis/citation/CBB001214200/)

Article María de Paz; (2018)
From Jurisprudence to Mechanics: Jacobi, Reech, and Poincaré on Convention (/isis/citation/CBB809116238/)

Article Thomas William Barrett; (2015)
On the Structure of Classical Mechanics (/isis/citation/CBB188856810/)

Chapter Luigi Pepe; (2015)
Lagrange tra meccanica e analisi (/isis/citation/CBB154068535/)

Book O'Shea, Donal; (2007)
The Poincaré Conjecture: In Search of the Shape of the Universe (/isis/citation/CBB000773353/)

Chapter Petitgirard, Loïc; (2006)
Poincaré, Précurseur du “chaos”? (/isis/citation/CBB001024284/)

Book Ebbinghaus, Heinz-Dieter; Peckhaus, Volker; (2007)
Ernst Zermelo: An Approach to His Life and Work (/isis/citation/CBB000831311/)

Book Charpentier, Éric; Ghys, Étienne; Lesne, Annick; (2010)
The Scientific Legacy of Poincaré (/isis/citation/CBB001023244/)

Chapter Tom Archibald; (2015)
Saturn’s Rings from Laplace to Poincaré (/isis/citation/CBB776089038/)

Book Christian Gerini; Jean-Marc Ginoux; (2013)
Henri Poincaré: A Biography Through the Daily Papers (/isis/citation/CBB354216167/)

Book Ferdinand Verhulst; (2012)
Henri Poincaré: Impatient Genius (/isis/citation/CBB160508794/)

Chapter Jeremy Gray; (2015)
Henri Poincaré and Hermann Weyl on the Foundations of Mathematics (/isis/citation/CBB501271170/)

Article Lizhen Ji; Chang Wang; (2020)
Poincaré’s stated motivations for topology (/isis/citation/CBB272091949/)

Article Lizhen Ji; Chang Wang; (2022)
Poincaré’s works leading to the Poincaré conjecture (/isis/citation/CBB001593509/)

Article German A. Duarte; (2017)
"Analysis Situs." A Survey of Spaces en devenir (/isis/citation/CBB765530267/)

Authors & Contributors
Ji, Lizhen
Wang, Chang
Archibald, Tom
Charpentier, Éric
Coutinho, S. C.
Ebbinghaus, Heinz-Dieter
Journals
Archive for History of Exact Sciences
Revue d'Histoire des Mathématiques
British Journal for the Philosophy of Science
Science in Context
Azimuth
Publishers
Springer International
American Mathematical Society
Birkhäuser
Springer
Springer Science + Business Media
Walker & Company
Concepts
Mathematics
Physics
Mathematical physics
Biographies
Celestial mechanics
Mechanics
People
Poincaré, Jules Henri
Hamilton, William Rowan
Lagrange, Joseph Louis
Bergson, Henri Louis
Hill, George William
Jacobi, Carl Gustav J.
Time Periods
19th century
20th century, early
18th century
20th century
Enlightenment
Places
Europe
France
Germany
Italy
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment