Lagrangian equations of motion for a massive conductor in a magnetic field

1994 ◽  
Vol 37 (7) ◽  
pp. 651-656
Author(s):  
Yu. G. Pavlenko ◽  
Yu. M. Petrov
Keyword(s):  
Magnetic Field ◽  
Equations Of Motion ◽  
Lagrangian Equations

Lagrangian equations of motion. Conservation laws

2020 ◽  
pp. 156-174
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Conservation Laws ◽  
Coordinate Transformation ◽  
Virial Theorem ◽  
Equations Of Motion ◽  
Electromechanical System ◽  
Interacting Particles ◽  
Integral Of Motion ◽  
Lagrangian Functions ◽  
Lagrangian Equations

This chapter addresses the invariance of the Lagrangian equations of motion under the coordinate to transformation, the transformation of the energy and generalised momenta under the coordinate transformation. The integrals of motion for a particle moving in the field with a given symmetry to the Noether’s theorem, the Lagrangian functions, and the Lagrangian equations of motion for the electromechanical system. The authors also discuss the influence of constraints and friction on the motion of a system, the virial theorem and its generalization in the presents of a magnetic field, and an additional integral of motion for a system of three interacting particles.

Lagrangian equations of motion. Conservation laws

2020 ◽  
pp. 16-24
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Conservation Laws ◽  
Coordinate Transformation ◽  
Virial Theorem ◽  
Equations Of Motion ◽  
Electromechanical System ◽  
Interacting Particles ◽  
Integral Of Motion ◽  
Lagrangian Functions ◽  
Lagrangian Equations

This chapter addresses the invariance of the Lagrangian equations of motion under the coordinate to transformation, the transformation of the energy and generalised momenta under the coordinate transformation. The integrals of motion for a particle moving in the field with a given symmetry to the Noether’s theorem, the Lagrangian functions, and the Lagrangian equations of motion for the electromechanical system. The authors also discuss the influence of constraints and friction on the motion of a system, the virial theorem and its generalization in the presents of a magnetic field, and an additional integral of motion for a system of three interacting particles.

scholarly journals Dynamics of an orbital polarization of twisted electron beams in electric and magnetic fields

2019 ◽  
Vol 204 ◽  
pp. 10008
Author(s):  
Alexander J. Silenko ◽  
Pengming Zhang ◽  
Liping Zou
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Magnetic Fields ◽  
Quantum Dynamics ◽  
Electron Beams ◽  
Equations Of Motion ◽  
Vortex Beam ◽  
Dirac Particles ◽  
Electric And Magnetic Fields ◽  
Average Projection

Relativistic classical and quantum dynamics of twisted (vortex) Dirac particles in arbitrary electric and magnetic fields is constructed. The relativistic Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived. Methods for the extraction of an electron vortex beam with a given orbital polarization and for the manipulation of such a beam are developed. The new effect of a radiative orbital polarization of a twisted electron beam in a magnetic field resulting in a nonzero average projection of the intrinsic orbital angular momentum on the field direction is predicted.

Magnetic Field-Induced Nonlinear Vibration of an Unbalanced Rotor

2003 ◽  
Author(s):  
Yuefang Wang ◽  
Ganyun Sun ◽  
Lihua Huang
Keyword(s):  
Magnetic Field ◽  
Potential Energy ◽  
Analytic Solution ◽  
Equations Of Motion ◽  
Oscillatory System ◽  
Forced Vibrations ◽  
Electric Motors ◽  
Jump Phenomenon ◽  
Mass Unbalance ◽  
Unbalanced Rotor

The free and forced flexural vibrations are investigated for rotors of electric motors operating in unsymmetrical magnetic fields. The magnetic potential energy reserved in the air-gap is analytically derived and the unbalanced magnetic pull is obtained through the law of energy conservation. With this excitation, the equations of motion of the unbalanced rotor are developed for nonlinear displacements response. For small dynamic eccentricities, the equations of motion are simplified and the rotor is compared to a free Duffing oscillatory system. The analytic solution for forced vibrations subject to residual mass-unbalance excitations is also obtained. Jump phenomenon in the solution is pointed out, and the effects of initial eccentricity and flux density on the natural frequency are also investigated.

Magnons Heat Transfer and Magnons Scattering in Magnetic Sandwich Lattices: Application to Fe/Gd(5)/Fe System

SPIN ◽  
2016 ◽  
Vol 06 (03) ◽  
pp. 1650007 ◽  
Author(s):  
Boualem Bourahla ◽  
Ouahiba Nafa
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Cross Sections ◽  
Thermal Transport ◽  
Magnetic Order ◽  
Equations Of Motion ◽  
Matching Method ◽  
Spatially Inhomogeneous ◽  
Coherent Transmission ◽  
Transmission And Reflection

A model calculation is presented for the coherent magnon transmission and thermal transport at ferromagnetic nanojunction boundaries. The system consists of a Gd ultrathin film sandwiched between two Fe semi-infinite ferromagnetically ordered crystals. The dynamic of the system is analyzed using the equations of motion for the spin precession amplitudes on the lattice sites, valid for the range of temperatures of interest. The coherent transmission and reflection cross sections at the nanojunction boundary are calculated using the matching method. These calculations are presented for arbitrary directions on the boundary, for all accessible frequencies in the propagating bands, at variable temperatures and for a given thicknesses of the ultrathin nanojunction, with no externally applied magnetic field. The model is applied in particular to the Fe/Gd(5)/Fe system with a ferromagnetic Gd nanojunction. Our model yields the total integrated coherent thermal conductivity due to coherent magnons transmission via the sandwiched five Gd spin layers of the nanojunction. It elucidates, in particular, the dependence of the coherent magnons transmission and thermal transport in relation to the spatially inhomogeneous magnetic order of the atomic planes of the nanojunction for a given thickness.

Two-dimensional motion of a parabolically confined charged particle in a perpendicular magnetic field

Open Physics ◽  
2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Orion Ciftja
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Equations Of Motion ◽  
Complex Variables ◽  
Perpendicular Magnetic Field ◽  
Two Dimensional ◽  
Cyclotron Motion ◽  
Lissajous Figures ◽  
Long Time ◽  
Concentric Circles

AbstractThe classical two-dimensional motion of a parabolically confined charged particle in presence of a perpendicular magnetic is studied. The resulting equations of motion are solved exactly by using a mathematical method which is based on the introduction of complex variables. The two-dimensional motion of a parabolically charged particle in a perpendicular magnetic field is strikingly different from either the two-dimensional cyclotron motion, or the oscillator motion. It is found that the trajectory of a parabolically confined charged particle in a perpendicular magnetic field is closed only for particular values of cyclotron and parabolic confining frequencies that satisfy a given commensurability condition. In these cases, the closed paths of the particle resemble Lissajous figures, though significant differences with them do exist. When such commensurability condition is not satisfied, path of particle is open and motion is no longer periodic. In this case, after a sufficiently long time has elapsed, the open paths of the particle fill a whole annulus, a region lying between two concentric circles of different radii.

scholarly journals Non-geodesic orbital and epicyclic frequencies in vicinity of slowly rotating magnetized neutron stars

2012 ◽  
Vol 8 (S290) ◽  
pp. 185-186
Author(s):  
Pavel Bakala ◽  
Martin Urbanec ◽  
Eva Šrámková ◽  
Zdeněk Stuchlík ◽  
Gabriel Török
Keyword(s):  
Magnetic Field ◽  
Neutron Stars ◽  
Equations Of Motion ◽  
Solution Of Equations ◽  
Test Particles ◽  
Perturbative Method ◽  
Relativistic Approach ◽  
Charged Test ◽  
The Magnetic Field

AbstractWe study non-geodesic corrections to the quasicircular motion of charged test particles in the field of magnetized slowly rotating neutron stars. The gravitational field is approximated by the Lense-Thirring geometry, the magnetic field is of the standard dipole character. Using a fully-relativistic approach we determine influence of the electromagnetic interaction (both attractive and repulsive) on the quasicircular motion. We focus on the behaviour of the orbital and epicyclic frequencies of the motion. Components of the four-velocity of the orbiting charged test particles are obtained by numerical solution of equations of motion, the epicyclic frequencies are obtained by using the standard perturbative method. The role of the combined effect of the neutron star magnetic field and its rotation in the character of the orbital and epicyclic frequencies is discussed.

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