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The Lagrange Configuration in Celestial Mechanics
Author(s) -
Littlewood J. E.
Publication year - 1960
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-10.1.640-t
Subject(s) - mathematics , mathematical proof , calculus (dental) , algebra over a field , mathematical economics , pure mathematics , geometry , medicine , dentistry
(2) Whittaker says that his work is based essentially on that of Delaunay in his Lunar Theory. This has a claim to be a great pioneering advance; but, as Mr. Swinnerton‐Dyer has just discovered, and pointed out to me, the proofs are not at all rigorous (nor is Whittaker's work on the ‘Adelphic integral’, which takes the same background for granted). It is not merely a question of refinement of convergence arguments; the step by step process fails at a certain point for lack of a general identity to support it, and to supply this is not at all trivial. Mr. Swinnerton‐Dyer, who read my first paper in manuscript (like me in ignorance of Whittaker's work), proved a theorem about equations with a Hamiltonian, and this covers Whittaker's results. His paper should appear in due course.