Geodesic
On the inverse variational problem in nonholonomic mechanics
Communications in Mathematics, Tome 20 (2012) no. 1, pp. 41-62.

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

The inverse problem of the calculus of variations in a nonholonomic setting is studied. The concept of constraint variationality is introduced on the basis of a recently discovered nonholonomic variational principle. Variational properties of first order mechanical systems with general nonholonomic constraints are studied. It is shown that constraint variationality is equivalent with the existence of a closed representative in the class of 2-forms determining the nonholonomic system. Together with the recently found constraint Helmholtz conditions this result completes basic geometric properties of constraint variational systems. A few examples of constraint variational systems are discussed.
Classification : 49N45, 58E30, 70F25
Keywords: inverse problem of the calculus of variations; Helmholtz conditions; nonholonomic constraints; the nonholonomic variational principle; constraint Euler-Lagrange equations; constraint Helmholtz conditions; constraint Lagrangian; constraint ballistic motion; relativistic particle 
@article{COMIM_2012__20_1_a5,
     author = {Rossi, Olga and Musilov\'a, Jana},
     title = {On the inverse variational problem in nonholonomic mechanics},
     journal = {Communications in Mathematics},
     pages = {41--62},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2012},
     mrnumber = {3001631},
     zbl = {06202718},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2012__20_1_a5/}
}
TY  - JOUR
AU  - Rossi, Olga
AU  - Musilová, Jana
TI  - On the inverse variational problem in nonholonomic mechanics
JO  - Communications in Mathematics
PY  - 2012
SP  - 41
EP  - 62
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/COMIM_2012__20_1_a5/
LA  - en
ID  - COMIM_2012__20_1_a5
ER  - 
%0 Journal Article
%A Rossi, Olga
%A Musilová, Jana
%T On the inverse variational problem in nonholonomic mechanics
%J Communications in Mathematics
%D 2012
%P 41-62
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/COMIM_2012__20_1_a5/
%G en
%F COMIM_2012__20_1_a5
Rossi, Olga; Musilová, Jana. On the inverse variational problem in nonholonomic mechanics. Communications in Mathematics, Tome 20 (2012) no. 1, pp. 41-62. http://geodesic.mathdoc.fr/item/COMIM_2012__20_1_a5/