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

Research output: Contribution to journalArticleResearchpeer-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 languageEnglish
Pages (from-to)965-967
JournalInternational Journal of Non-Linear Mechanics
Volume47
Issue number9
DOIs
Publication statusPublished - 1 Nov 2012

Keywords

  • Analytic first integrals
  • Charged particle
  • Magnetic field
  • Polynomial first integrals

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