Noether symmetries for two-dimensional charged particle motion

Abstract

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 satisfy 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.

References in corpus (1)

• Invariant Variation Problems

Cited by in corpus (5)

• Dynamical symmetries and the Ermakov invariant
• Symmetries of charged particle motion under time-independent electromagnetic fields
• Lie symmetries for two-dimensional charged particle motion
• Group classification of charged particle motion in stationary electromagnetic fields
• Frobenius theorem and invariants for Hamiltonian systems