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Noether symmetries for two-dimensional charged particle motion

F Haas and J Goedert

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We find the Noether point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries are composed of a quasi-invariance transformation, a time-dependent rotation and a time-dependent spatial translation. The associated electromagnetic field satisfies a system of first-order linear partial differential equations. This system is solved exactly, yielding three classes of electromagnetic fields compatible with Noether point symmetries. The corresponding Noether invariants are derived and interpreted.


PACS

45.50.Dd General motion

02.30.Jr Partial differential equations

02.30.Em Potential theory

45.20.Jj Lagrangian and Hamiltonian mechanics

MSC

78A35 Motion of charged particles

70H03 Lagrange's equations

35F05 General theory of linear first-order PDE

82C05 Classical dynamic and nonequilibrium statistical mechanics (general)

Subjects

Mathematical physics

Dates

Issue 39 (1 October 1999)

Received 3 July 1999



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