Symmetries of a dynamical system represented by singular Lagrangians

Havelková, Monika. "Symmetries of a dynamical system represented by singular Lagrangians." Communications in Mathematics 20.1 (2012): 23-32. <http://eudml.org/doc/246138>.

@article{Havelková2012,
abstract = {Dynamical properties of singular Lagrangian systems differ from those of classical Lagrangians of the form $L=T-V$. Even less is known about symmetries and conservation laws of such Lagrangians and of their corresponding actions. In this article we study symmetries and conservation laws of a concrete singular Lagrangian system interesting in physics. We solve the problem of determining all point symmetries of the Lagrangian and of its Euler-Lagrange form, i.e. of the action. It is known that every point symmetry of a Lagrangian is a point symmetry of its Euler-Lagrange form, and this of course happens also in our case. We are also interested in the converse statement, namely if to every point symmetry $\xi $ of the Euler-Lagrange form $E$ there exists a Lagrangian $\lambda $ for $E$ such that $\xi $ is a point symmetry of $\lambda $. In the case studied the answer is affirmative, moreover we have found that the corresponding Lagrangians are all of order one.},
author = {Havelková, Monika},
journal = {Communications in Mathematics},
keywords = {singular Lagrangians; Euler-Lagrange form; point symmetry; conservation law; equivalent Lagrangians; singular Lagrangians; Euler-Lagrange form; point symmetry; conservation law; equivalent Lagrangians},
language = {eng},
number = {1},
pages = {23-32},
publisher = {University of Ostrava},
title = {Symmetries of a dynamical system represented by singular Lagrangians},
url = {http://eudml.org/doc/246138},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Havelková, Monika
TI - Symmetries of a dynamical system represented by singular Lagrangians
JO - Communications in Mathematics
PY - 2012
PB - University of Ostrava
VL - 20
IS - 1
SP - 23
EP - 32
AB - Dynamical properties of singular Lagrangian systems differ from those of classical Lagrangians of the form $L=T-V$. Even less is known about symmetries and conservation laws of such Lagrangians and of their corresponding actions. In this article we study symmetries and conservation laws of a concrete singular Lagrangian system interesting in physics. We solve the problem of determining all point symmetries of the Lagrangian and of its Euler-Lagrange form, i.e. of the action. It is known that every point symmetry of a Lagrangian is a point symmetry of its Euler-Lagrange form, and this of course happens also in our case. We are also interested in the converse statement, namely if to every point symmetry $\xi $ of the Euler-Lagrange form $E$ there exists a Lagrangian $\lambda $ for $E$ such that $\xi $ is a point symmetry of $\lambda $. In the case studied the answer is affirmative, moreover we have found that the corresponding Lagrangians are all of order one.
LA - eng
KW - singular Lagrangians; Euler-Lagrange form; point symmetry; conservation law; equivalent Lagrangians; singular Lagrangians; Euler-Lagrange form; point symmetry; conservation law; equivalent Lagrangians
UR - http://eudml.org/doc/246138
ER -