Relativistic dynamics of a spinning magnetic particle

1942 ◽  
Vol 38 (1) ◽  
pp. 40-60 ◽  
Author(s):  
Myron Mathisson
Keyword(s):  
Angular Momentum ◽  
Magnetic Particle ◽  
Magnetic Moments ◽  
Equations Of Motion ◽  
Energy Tensor ◽  
Centre Of Mass ◽  
Electric Moment ◽  
Electric And Magnetic Moments ◽  
Second Moments ◽  
External Forces

The author's general variational method is applied to the case of a particle for which second moments are important but third and higher moments are negligible. Equations of motion are obtained for the angular momentum and for the centre of mass, equations (12·35) and (12·41), with arbitrary external forces X.The angular forces are then calculated for a charged particle with electric and magnetic moments moving in a general electromagnetic field, on the assumption that the effect of a certain part of the energy tensor, Tiii of (15·17), is negligible. This leads to the equations of angular motion, (17·13), from which it is inferred that, in order that the magnitude of the angular momentum may be integrable, the angular momentum, electric and magnetic moments must all be parallel in a frame of reference in which the particle is instantaneously at rest.The linear forces are then calculated for the case of no electric moment, leading to the equations for linear motion (18·10). From these it is inferred that, in order that the mass may be integrable, the ratio of the magnetic moment to the angular momentum must be constant.

scholarly journals Numerical methods for General Relativistic particles

2018 ◽  
Vol 14 (S342) ◽  
pp. 19-23
Author(s):  
Fabio Bacchini ◽  
Bart Ripperda ◽  
Alexander Y. Chen ◽  
Lorenzo Sironi
Keyword(s):  
Numerical Methods ◽  
Gravitational Lensing ◽  
Complex Dynamics ◽  
Equations Of Motion ◽  
Numerical Algorithms ◽  
Relativistic Effects ◽  
Compact Objects ◽  
Light Rays ◽  
Massive Particles ◽  
External Forces

AbstractWe present recent developments on numerical algorithms for computing photon and particle trajectories in the surrounding of compact objects. Strong gravity around neutron stars or black holes causes relativistic effects on the motion of massive particles and distorts light rays due to gravitational lensing. Efficient numerical methods are required for solving the equations of motion and compute i) the black hole shadow obtained by tracing light rays from the object to a distant observer, and ii) obtain information on the dynamics of the plasma at the microscopic scale. Here, we present generalized algorithms capable of simulating ensembles of photons or massive particles in any spacetime, with the option of including external forces. The coupling of these tools with GRMHD simulations is the key point for obtaining insight on the complex dynamics of accretion disks and jets and for comparing simulations with upcoming observational results from the Event Horizon Telescope.

scholarly journals CHIRAL QUARK MODEL (χQM) AND THE NUCLEON SPIN

2004 ◽  
Vol 19 (29) ◽  
pp. 5027-5041 ◽  
Author(s):  
HARLEEN DAHIYA ◽  
MANMOHAN GUPTA
Keyword(s):  
Angular Momentum ◽  
Magnetic Moments ◽  
Distribution Functions ◽  
Gluon Polarization ◽  
Spin Distribution ◽  
Polarization Functions ◽  
Singlet Component ◽  
Configuration Mixing ◽  
The Right ◽  
E866 Data

Using χ QM with configuration mixing, the contribution of the gluon polarization to the flavor singlet component of the total spin has been calculated phenomenologically through the relation [Formula: see text] as defined in the Adler–Bardeen scheme, where ΔΣ on the right-hand side is Q2 independent. For evaluation the contribution of gluon polarization [Formula: see text], ΔΣ is found in the χ QM by fixing the latest E866 data pertaining to [Formula: see text] asymmetry and the spin polarization functions whereas ΔΣ(Q2) is taken to be 0.30±0.06 and αs=0.287±0.020, both at Q2=5 GeV 2. The contribution of gluon polarization Δg' comes out to be 0.33 which leads to an almost perfect fit for spin distribution functions in the χ QM . When its implications for magnetic moments are investigated, we find perfect fit for many of the magnetic moments. If an attempt is made to explain the angular momentum sum rule for proton by using the above value of Δg', one finds the contribution of gluon angular momentum to be as important as that of the [Formula: see text] pairs.

scholarly journals QUARK ORBITAL ANGULAR MOMENTUM IN THE BARYON

2001 ◽  
Vol 16 (22) ◽  
pp. 3673-3697 ◽  
Author(s):  
XIAOTONG SONG
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Orbital Motion ◽  
Magnetic Moments ◽  
Sum Rule ◽  
Quark Spin ◽  
Quark Flavor ◽  
Quark Orbital Angular Momentum ◽  
Quark Flavors ◽  
Partition Factor

Analytical and numerical results, for the orbital and spin content carried by different quark flavors in the baryons, are given in the chiral quark model with symmetry breaking. The reduction of the quark spin, due to the spin dilution in the chiral splitting processes, is transferred into the orbital motion of quarks and antiquarks. The orbital angular momentum for each quark flavor in the proton as a function of the partition factor κ and the chiral splitting probability a is shown. The cancellation between the spin and orbital contributions in the spin sum rule and in the baryon magnetic moments is discussed.

Orbital angular momentum-driven anomalous Hall effect

2021 ◽  
Author(s):  
Oliver Dowinton ◽  
Mohammad Bahramy
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Transition Metal Oxides ◽  
Magnetic State ◽  
Magnetic Moments ◽  
Anomalous Hall Effect ◽  
Ferromagnetic State ◽  
Periodic Systems ◽  
Spin States ◽  
Berry Curvature

Abstract Orbital angular momentum (OAM) plays a central role in regulating the magnetic state of electrons in non-periodic systems such as atoms and molecules. In solids, on the other hand, OAM is usually quenched by the crystal field, and thus, has a negligible effect on magnetisation. Accordingly, it is generally neglected in discussions around band topology such as Berry curvature (BC) and intrinsic anomalous Hall conductivity (AHC). Here, we present a theoretical framework demonstrating that crystalline OAM can be directionally unquenched in transition metal oxides via energetic proximity of the conducting d electrons to the local magnetic moments. We show that this leads to `composite' Fermi-pockets with topologically non-trivial OAM textures. This enables a giant Berry curvature with an intrinsic non-monotonic AHC, even in collinearly-ordered spin states. We use this model to explain the origin of the giant AHC observed in the forced-ferromagnetic state of EuTiO3 and propose it as a prototype for OAM driven AHC.

scholarly journals Simulation of a rotating strong gravity that reverses time

2021 ◽  
pp. 7-16
Author(s):  
Yoshio Matsuki ◽  
Petro Bidyuk
Keyword(s):  
Angular Momentum ◽  
Gravitational Field ◽  
Momentum Density ◽  
Polar Coordinates ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Strong Gravity ◽  
The Past ◽  
Stress Energy ◽  
The Future

In this research we simulated how time can be reversed with a rotating strong gravity. At first, we assumed that the time and the space can be distorted with the presence of a strong gravity, and then we calculated the angular momentum density of the rotating gravitational field. For this simulation we used Einstein’s field equation with spherical polar coordinates and the Euler’s transformation matrix to simulate the rotation. We also assumed that the stress-energy tensor that is placed at the end of the strong gravitational field reflects the intensities of the angular momentum, which is the normal (perpendicular) vector to the rotating axis. The result of the simulation shows that the angular momentum of the rotating strong gravity changes its directions from plus (the future) to minus (the past) and from minus (the past) to plus (the future), depending on the frequency of the rotation.

A Project in the Determination of the Moment of Inertia

2005 ◽  
Vol 33 (4) ◽  
pp. 319-338
Author(s):  
Ron P. Podhorodeski ◽  
Paul Sobejko
Keyword(s):  
Dynamic Properties ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Moment Of Inertia ◽  
Educational Goal ◽  
Centre Of Mass ◽  
Comparison Of Results ◽  
Physical Testing ◽  
The Moment

Analysis of the forces involved in mechanical systems requires an understanding of the dynamic properties of the system's components. In this work, a project on the determination of both the location of the centre of mass and inertial properties is described. The project involves physical testing, the proposal of approximate models, and the comparison of results. The educational goal of the project is to give students and appreciation of second mass moments and the validity of assumptions that are often applied in component modelling. This work reviews relevant equations of motion and discusses techniques to determine or estimate the centre of mass and second moment of inertia. An example project problem and solutions are presented. The value of such project problems within a first course on the theory of mechanisms is discussed.

Added Fluid Mass and the Equations of Motion of a Parachute

1983 ◽  
Vol 34 (3) ◽  
pp. 226-242 ◽  
Author(s):  
John A. Eaton
Keyword(s):  
Equations Of Motion ◽  
Added Mass ◽  
Unsteady Forces ◽  
Fluid Mass ◽  
Mass Tensor ◽  
Body Shapes ◽  
The Stability ◽  
External Forces ◽  
Six Degree Of Freedom ◽  
Nonlinear Solutions

SummaryWhile it has long been known that added fluid mass may be important in the dynamics of parachutes, due to inadequate or incorrect derivation and/or implementation of the added mass tensor its full significance in the stability of parachutes has yet to be appreciated. The concept of added mass is outlined and some general conditions for its significance are presented. Its implementation in the parachute equations of motion is reviewed, and the equations used in previous treatments are shown to be erroneous. A general method for finding the equivalent external forces and moments due to added mass is given, and the correct, anisotropic forms of the added mass tensor are derived for the six degree-of-freedom motion in an ideal fluid of rigid body shapes with planar-, twofold- and axisymmetry, These derivations may also be useful in dynamic stability studies of other low relative density bodies such as airships, balloons, submarines and torpedoes. Full nonlinear solutions of the equations of motion for the axisymmetric parachute have been obtained, and results indicate that added mass effects are more significant than previously predicted. In particular, the component of added mass along the axis of symmetry has a strong influence on stability. Better data on unsteady forces and moments on parachutes are needed.

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

AN ACTION PRINCIPLE FOR MAGNETOHYDRODYNAMICS

1963 ◽  
Vol 41 (12) ◽  
pp. 2241-2251 ◽  
Author(s):  
M. G. Calkin
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Magnetic Induction ◽  
Vector Potential ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Action Principle ◽  
Invariance Properties ◽  
Conservation Of Momentum

The equations of motion of an inviscid, infinitely conducting fluid in an electromagnetic field are transformed into a form suitable for an action principle. An action principle from which these equations may be derived is found. The conservation laws follow from invariance properties of the action. The space–time invariances lead to the conservation of momentum, energy, angular momentum, and center of mass, while the gauge invariances lead to conservation of mass, a generalization of the Helmholtz vortex theorem of hydrodyanmics, and the conservation of the volume integrals of A∙B and v∙B, where A is the vector potential, B is the magnetic induction, and v is the fluid velocity.

Sign in / Sign up

Export Citation Format

Share Document