First integrals for a charged particle moving on a plane under the action of a magnetic field orthogonal to this plane

Jaume Llibre; Clàudia Valls

doi:10.1016/j.ijnonlinmec.2012.07.001

First integrals for a charged particle moving on a plane under the action of a magnetic field orthogonal to this plane

Jaume Llibre, Clàudia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

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.

Original language	English
Pages (from-to)	965-967
Journal	International Journal of Non-Linear Mechanics
Volume	47
Issue number	9
DOIs	https://doi.org/10.1016/j.ijnonlinmec.2012.07.001
Publication status	Published - 1 Nov 2012

Keywords

Analytic first integrals
Charged particle
Magnetic field
Polynomial first integrals

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Llibre, J., & Valls, C. (2012). First integrals for a charged particle moving on a plane under the action of a magnetic field orthogonal to this plane. International Journal of Non-Linear Mechanics, 47(9), 965-967. https://doi.org/10.1016/j.ijnonlinmec.2012.07.001

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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

U2 - 10.1016/j.ijnonlinmec.2012.07.001

DO - 10.1016/j.ijnonlinmec.2012.07.001

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JF - International Journal of Non-Linear Mechanics

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