Geodesic
The inverse problem in the calculus of variations: new developments
Communications in Mathematics, Tome 29 (2021) no. 1, pp. 131-149

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 37J06, 49N45, 58A15, 70H03
Keywords: Inverse problem in the calculus of variations; Helmholtz conditions; Exterior differential systems; Lagrangian system. 
@article{COMIM_2021__29_1_a7,
     author = {Do, Thoan and Prince, Geoff},
     title = {The inverse problem in the calculus of variations: new developments},
     journal = {Communications in Mathematics},
     pages = {131--149},
     publisher = {mathdoc},
     volume = {29},
     number = {1},
     year = {2021},
     mrnumber = {4251311},
     zbl = {07413361},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2021__29_1_a7/}
}
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
SP  - 131
EP  - 149
VL  - 29
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/COMIM_2021__29_1_a7/
LA  - en
ID  - COMIM_2021__29_1_a7
ER  - 
%0 Journal Article
%A Do, Thoan
%A Prince, Geoff
%T The inverse problem in the calculus of variations: new developments
%J Communications in Mathematics
%D 2021
%P 131-149
%V 29
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/COMIM_2021__29_1_a7/
%G en
%F COMIM_2021__29_1_a7
Do, Thoan; Prince, Geoff. The inverse problem in the calculus of variations: new developments. Communications in Mathematics, Tome 29 (2021) no. 1, pp. 131-149. http://geodesic.mathdoc.fr/item/COMIM_2021__29_1_a7/