MOVING FRAMES AND NOETHER’S CONSERVATION LAWS—THE GENERAL CASE
Forum of Mathematics, Sigma, Tome 4 (2016)
Voir la notice de l'article provenant de la source Cambridge University Press
In recent works [Gonçalves and Mansfield, Stud. Appl. Math., 128 (2012), 1–29; Mansfield, A Practical Guide to the Invariant Calculus (Cambridge University Press, Cambridge, 2010)], the authors considered various Lagrangians, which are invariant under a Lie group action, in the case where the independent variables are themselves invariant. Using a moving frame for the Lie group action, they showed how to obtain the invariantized Euler–Lagrange equations and the space of conservation laws in terms of vectors of invariants and the Adjoint representation of a moving frame. In this paper, we show how these calculations extend to the general case where the independent variables may participate in the action. We take for our main expository example the standard linear action of SL(2) on the two independent variables. This choice is motivated by applications to variational fluid problems which conserve potential vorticity. We also give the results for Lagrangians invariant under the standard linear action of SL(3) on the three independent variables.
@article{10_1017_fms_2016_24,
author = {T\^ANIA M. N. GON\c{C}ALVES and ELIZABETH L. MANSFIELD},
title = {MOVING {FRAMES} {AND} {NOETHER{\textquoteright}S} {CONSERVATION} {LAWS{\textemdash}THE} {GENERAL} {CASE}},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {4},
year = {2016},
doi = {10.1017/fms.2016.24},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2016.24/}
}
TY - JOUR AU - TÂNIA M. N. GONÇALVES AU - ELIZABETH L. MANSFIELD TI - MOVING FRAMES AND NOETHER’S CONSERVATION LAWS—THE GENERAL CASE JO - Forum of Mathematics, Sigma PY - 2016 VL - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2016.24/ DO - 10.1017/fms.2016.24 LA - en ID - 10_1017_fms_2016_24 ER -
%0 Journal Article %A TÂNIA M. N. GONÇALVES %A ELIZABETH L. MANSFIELD %T MOVING FRAMES AND NOETHER’S CONSERVATION LAWS—THE GENERAL CASE %J Forum of Mathematics, Sigma %D 2016 %V 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2016.24/ %R 10.1017/fms.2016.24 %G en %F 10_1017_fms_2016_24
TÂNIA M. N. GONÇALVES; ELIZABETH L. MANSFIELD. MOVING FRAMES AND NOETHER’S CONSERVATION LAWS—THE GENERAL CASE. Forum of Mathematics, Sigma, Tome 4 (2016). doi: 10.1017/fms.2016.24
Cité par Sources :