TY - JOUR
T1 - First integrals for a charged particle moving on a plane under the action of a magnetic field orthogonal to this plane
AU - Llibre, Jaume
AU - Valls, Clàudia
PY - 2012/11/1
Y1 - 2012/11/1
N2 - We characterize the polynomial (respectively analytical) first integrals of degree one in the variables u and v of the differential systems of the form x′=u, y′=v, u′=B(x,y)v and v′=-B(x,y)u where B=B(x,y) is a polynomial (respectively analytic function) in the variables x and y. This differential system models a non-relativistic charge moving on a plane under the action of a magnetic field orthogonal to this plane. © 2012 Elsevier Ltd. All rights reserved.
AB - We characterize the polynomial (respectively analytical) first integrals of degree one in the variables u and v of the differential systems of the form x′=u, y′=v, u′=B(x,y)v and v′=-B(x,y)u where B=B(x,y) is a polynomial (respectively analytic function) in the variables x and y. This differential system models a non-relativistic charge moving on a plane under the action of a magnetic field orthogonal to this plane. © 2012 Elsevier Ltd. All rights reserved.
KW - Analytic first integrals
KW - Charged particle
KW - Magnetic field
KW - Polynomial first integrals
UR - https://ddd.uab.cat/record/150509
U2 - https://doi.org/10.1016/j.ijnonlinmec.2012.07.001
DO - https://doi.org/10.1016/j.ijnonlinmec.2012.07.001
M3 - Article
VL - 47
SP - 965
EP - 967
JO - International Journal of Non-Linear Mechanics
JF - International Journal of Non-Linear Mechanics
SN - 0020-7462
IS - 9
ER -