2 Noether symmetries for two - dimensional charged particle motion
نویسندگان
چکیده
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.
منابع مشابه
Noether Symmetries for Charged Particle Motion under a Magnetic Monopole and General Electric Fields
The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely solved when the magnetic field is produced by a fixed magnetic monopole. The result is applied to central electric field cases, in particular to the time-depen...
متن کامل2 Lie symmetries for two - dimensional charged particle motion
We find the Lie point symmetries for non–relativistic two-dimensional charged particle motion. These symmetries comprise a quasi–inva-riance transformation, a time–dependent rotation, a time–dependent spatial translation and a dilatation. The associated electromagnetic fields satisfy a system of first–order linear partial differential equations. This system is solved exactly, yielding four clas...
متن کاملTwo-dimensional systems that arise from the Noether classification of Lagrangians on the line
Noether-like operators play an essential role in writing down the first integrals for Euler-Lagrange systems of ordinary differential equations (ODEs). The classification of such operators is carried out with the help of analytic continuation of Lagrangians on the line. We obtain the classification of 5, 6 and 9 Noether-like operators for two-dimensional Lagrangian systems that arise from the s...
متن کاملSystematic Derivation of Noether Point Symmetries in Special Relativistic Field Theories
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real s...
متن کاملNon-Noether symmetries and conserved quantities of nonconservative dynamical systems
This Letter focuses on studying non-Noether symmetries and conserved quantities of the nonconservative dynamical system. Based on the relationships among motion, nonconservative forces and Lagrangian, we present conservation laws on non-Noether symmetries for nonconservative dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry in nonconservative sys...
متن کامل