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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The inverse problem of the calculus of variations: The use of geometrical calculus in Douglas’s analysis
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by W. Sarlet, G. Thompson and G. E. Prince PDF
Trans. Amer. Math. Soc. 354 (2002), 2897-2919 Request permission

Abstract:

The main objective of this paper is to work out a full-scale application of the integrability analysis of the inverse problem of the calculus of variations, as developed in recent papers by Sarlet and Crampin. For this purpose, the celebrated work of Douglas on systems with two degrees of freedom is taken as the reference model. It is shown that the coordinate-free, geometrical calculus used in Sarlet and Crampin’s general theoretical developments provides effective tools also to do the practical calculations. The result is not only that all subcases distinguished by Douglas can be given a more intrinsic characterization, but also that in most of the cases, the calculations can be carried out in a more efficient way and often lead to sharper conclusions.
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Additional Information
  • W. Sarlet
  • Affiliation: Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281, B-9000 Ghent, Belgium
  • Email: willy.sarlet@rug.ac.be
  • G. Thompson
  • Affiliation: Department of Mathematics, The University of Toledo, Toledo, Ohio 43606
  • Email: gthomps@uoft02.utoledo.edu
  • G. E. Prince
  • Affiliation: School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia
  • Address at time of publication: Department of Mathematics, La Trobe University, Victoria 3086, Australia
  • MR Author ID: 142145
  • ORCID: 0000-0003-4819-2219
  • Email: g.prince@latrobe.edu.au
  • Received by editor(s): October 25, 2000
  • Published electronically: March 14, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2897-2919
  • MSC (2000): Primary 37J05, 70H03; Secondary 49N45
  • DOI: https://doi.org/10.1090/S0002-9947-02-02994-X
  • MathSciNet review: 1895208