The inception of Symplectic Geometry: the works of Lagrange and Poisson during the years 1808-1810

Charles-Michel Marle (1)

1 IMJ - Institut de Mathématiques de Jussieu

The concept of a symplectic structure first appeared in the works of Lagrange on the so-called "method of variation of the constants". These works are presented, together with those of Poisson, who first defined the composition law called today the "Poisson bracket". The method of variation of the constants is presented using today's mathematical concepts and notations.

Domaines: Histoire et perspectives sur les mathématiques [math.HO]; Géométrie différentielle [math.DG]

Charles-Michel Marle. The inception of Symplectic Geometry: the works of Lagrange and Poisson during the years 1808-1810. Letters in Mathematical Physics, 2009, 90, pp.3--21. ⟨10.1007/s11005-009-0347-y⟩. ⟨hal-00940263⟩