The inverse problem in the calculus of variations: new developments

Thoan Do; Geoff Prince

Communications in Mathematics (2021)

  • Issue: 1, page 131-149
  • ISSN: 1804-1388

Abstract

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We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of n second order ordinary differential equations. A number of recent theorems are presented, using exterior differential systems theory (EDS). In particular, we indicate how to generalise Jesse Douglas’s famous solution for n = 2 . We then examine a new class of solutions in arbitrary dimension n and give some non-trivial examples in dimension 3.

How to cite

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Do, Thoan, and Prince, Geoff. "The inverse problem in the calculus of variations: new developments." Communications in Mathematics (2021): 131-149. <http://eudml.org/doc/297545>.

@article{Do2021,
abstract = {We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of $n$ second order ordinary differential equations. A number of recent theorems are presented, using exterior differential systems theory (EDS). In particular, we indicate how to generalise Jesse Douglas’s famous solution for $n=2$. We then examine a new class of solutions in arbitrary dimension $n$ and give some non-trivial examples in dimension 3.},
author = {Do, Thoan, Prince, Geoff},
journal = {Communications in Mathematics},
keywords = {Inverse problem in the calculus of variations; Helmholtz conditions; Exterior differential systems; Lagrangian system},
language = {eng},
number = {1},
pages = {131-149},
publisher = {University of Ostrava},
title = {The inverse problem in the calculus of variations: new developments},
url = {http://eudml.org/doc/297545},
year = {2021},
}

TY - JOUR
AU - Do, Thoan
AU - Prince, Geoff
TI - The inverse problem in the calculus of variations: new developments
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
IS - 1
SP - 131
EP - 149
AB - We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of $n$ second order ordinary differential equations. A number of recent theorems are presented, using exterior differential systems theory (EDS). In particular, we indicate how to generalise Jesse Douglas’s famous solution for $n=2$. We then examine a new class of solutions in arbitrary dimension $n$ and give some non-trivial examples in dimension 3.
LA - eng
KW - Inverse problem in the calculus of variations; Helmholtz conditions; Exterior differential systems; Lagrangian system
UR - http://eudml.org/doc/297545
ER -

References

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