Article ID: CBB563006808

Canonical transformations from Jacobi to Whittaker (2023)


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.

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Authors & Contributors
Wang, Chang
Ji, Lizhen
Thomas William Barrett
Christian Gerini
Duarte, German A.
Paz, María de
Archive for History of Exact Sciences
Revue d'Histoire des Mathématiques
Science in Context
Historia Mathematica
British Society for the History of Mathematics Bulletin
World Scientific
Springer Science + Business Media
Springer International
Princeton University Press
Algebraic topology
Poincaré, Jules Henri
Laplace, Pierre Simon
Hamilton, William Rowan
Weierstrass, Karl Theodor
Darwin, George Howard
Zermelo, Ernst
Time Periods
19th century
20th century, early
18th century
20th century

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