The origins of symplectic calculus in Lagrange's work
type: Item
instance of: scholarly article
title: The origins of symplectic calculus in Lagrange's work
zbMATH Open document ID: 0966.01017
published in: L'Enseignement Mathématique. 2e Série
publication date: 2001-01-30T00:00:00Z
review text: Since Kepler ephemerides of a planet were no question but there was no general approach to the global problem of real movements within the whole planetary system. To that end Lagrange has invented in 1808-1811 a method of variations of constants. In order to describe the movement of one planet around the Sun (solving a second order differential equation) one needs 6 constants but an instantaneous shock (e.g., impact of an asteroid) yields another 6 constants which describe the movement of that planet along another ellipse. Lagrange considered interactions of other planets within the system as a series of infinitesimal and continuous shocks. In that way he came to a differentiable description of a perturbated planet as a curve in the space of all Keplerian movements. And it was here that a symplectic structure appeared for the first time (the term ``symplectic'' has been, however, introduced by Hermann Weyl only in 1946). The paper is a fine reconstruction of Lagrange's procedures.
reviewed by: Roman Duda
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 37-03
Mathematics Subject Classification ID: 53-03
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 70-03
zbMATH DE Number: 1558728
zbMATH Keywords: method of variations of constants
zbMATH Keywords: Hermann Weyl
author: Patrick Iglesias-Zemmour
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1558728