Symmetry of equations of motion for a free particle in riemann space

1975 ◽  
Vol 18 (12) ◽  
pp. 1650-1654 ◽  
Author(s):  
V. N. Shapovalov
Keyword(s):  
Equations Of Motion ◽  
Free Particle ◽  
Riemann Space

scholarly journals The Boltzmann Equations in General Relativity

1936 ◽  
Vol 4 (4) ◽  
pp. 238-253 ◽  
Author(s):  
A. G. Walker
Keyword(s):  
General Relativity ◽  
Continuous Medium ◽  
Equations Of Motion ◽  
Free Particle ◽  
Energy Tensor ◽  
Principle Of Equivalence ◽  
Boltzmann Equations ◽  
Conservation Equations ◽  
Proper Mass ◽  
Conservation Of Momentum

In a recent paper, J. L. Synge gives an interesting derivation of the conservation equations Tij,j = 0 satisfied by the energy tensor Tij of a continuous medium. Previous to the appearance of this paper, these equations were generally obtained by assuming the classical equations of motion and continuity, after which it was necessary to appeal to the Principle of Equivalence. It then follows that the path of a free particle is a geodesic. Synge however starts with the hypothesis that the path of a particle between collisions is a geodesic and that the proper mass is constant. The conservation equations are then deduced exactly from the law of conservation of momentum for collisions.

Green’s function for an electron model with a plane wave

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Hassen Ould Lahoucine ◽  
Lyazid Chetouani
Keyword(s):  
Green Function ◽  
Plane Wave ◽  
Path Integral ◽  
Equations Of Motion ◽  
Free Particle ◽  
Dirac Particle ◽  
Integral Approach ◽  
Electron Model ◽  
Plane Wave Field ◽  
The Green Function

AbstractThe Green function for a Dirac particle subject to a plane wave field is constructed according to the path integral approach and the Barut’s electron model. Then it is exactly determined after having fixed a matrix U chosen so that the equations of motion are those of a free particle, and by using the properties of the plane wave and also with some shifts.

scholarly journals Movimiento caótico de partículas libres que viajan sobre guías de ondas bajo un potencial eléctrico apantallado

2019 ◽  
pp. 1-4
Keyword(s):  
Chaotic Behavior ◽  
Characteristic Point ◽  
Equations Of Motion ◽  
Free Particle ◽  
Electrical Potential ◽  
Hamiltonian Function ◽  
Nonlinear Dynamic System ◽  
Autonomous Function ◽  
El Sistema ◽  
Potential Perturbation

Movimiento caótico de partículas libres que viajan sobre guías de ondas bajo un potencial eléctrico apantallado Free particle chaotic motion traveling on a low waveguides Shielded electrical potential C. Moya Egoavil, J. Gutiérrez Garcia Facultad de Ciencias Departamento de Física– Universidad Nacional de Piura DOI: https://doi.org/10.33017/RevECIPeru2012.0001/ RESUMEN El estudio del comportamiento caótico en la dispersión y movimiento que presentan las partículas libres frente a un potencial apantallado dentro de un medio de guía de onda mesoscópica, se realizó el análisis de la función hamiltoniana adimensional conservativa trabajada en coordenadas conjugadas, representando y evaluando las trayectorias de estado en el espacio fásico, con un trazado topológico de Poincaré en puntos fijos característicos del sistema, en el origen x = 0 y en x = ±∞, y su estabilidad como sistema dinámico no lineal mediante las ecuaciones de movimiento de Hamilton. Mediante métodos numéricos se retrató la función autónoma de Hamilton conservativa no integrable, debido a la perturbación del potencial que se aplicó dentro del sistema, dándonos información para poder concluir que el sistema era inestable y que las orbitas que dibujan el espacio de estados, tienden a un comportamiento asintótico sobre un punto característico en x = 0, alejados de ellas no existe predecibilidad del desenvolvimiento espacial para estas partículas, esto significa caos a menor escala para poder describir físicamente su movimiento. Palabras claves: Hamiltoniana, topológico, Poincaré, perturbación. ABSTRACT The study of chaotic behavior in the dispersal and movement presented by free particles shielded against potential within half mesoscopic waveguide, we performed the analysis of the dimensionless Hamiltonian function retain workers in conjugate coordinates, representing and evaluating state trajectories in phase space with a topological path at fixed points of Poincare characteristic of the system, the origin x = 0 and x = ±∞, and its stability as a nonlinear dynamic system using the Hamilton equations of motion . By numerical analysis portrayed the autonomous function of Hamilton conservative nonintegrable due to potential perturbation within the system was applied, giving information to Stripper Arm the system was unstable and the orbits drawn by the state space, tend to asymptotic behavior on a characteristic point at x = 0, away from them there is no predictability of the development space for these particles, this means a smaller scale chaos to describe physical movement. Keywords: Hamiltonian, topological, Poincaré, perturbation.

scholarly journals PERFECT HYPERMOMENTUM FLUID: VARIATIONAL THEORY AND EQUATIONS OF MOTION

1998 ◽  
Vol 13 (31) ◽  
pp. 5391-5407 ◽  
Author(s):  
O. V. BABOUROVA ◽  
B. N. FROLOV
Keyword(s):  
Evolution Equation ◽  
Affine Space ◽  
Lagrangian Density ◽  
Hydrodynamic Equation ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Riemann Space ◽  
Variational Theory ◽  
Stress Energy ◽  
New Type

The variational theory of the perfect hypermomentum fluid is developed. The new type of the generalized Frenkel condition is considered. The Lagrangian density of such fluid is stated, and the equations of motion of the fluid and the Weyssenhoff-type evolution equation of the hypermomentum tensor are derived. The expressions of the matter currents of the fluid (the canonical energy–momentum three-form, the metric stress–energy four-form and the hypermomentum three-form) are obtained. The Euler-type hydrodynamic equation of motion of the perfect hypermomentum fluid is derived. It is proved that the motion of the perfect fluid without hypermomentum in a metric-affine space coincides with the motion of this fluid in a Riemann space.

Classical motion of a point particle with extrinsic curvature

1991 ◽  
Vol 69 (7) ◽  
pp. 830-832 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Equations Of Motion ◽  
Free Particle ◽  
Coulomb Field ◽  
Extrinsic Curvature ◽  
Point Particle ◽  
Moving Frame ◽  
Arc Length ◽  
Classical Motion ◽  
Time Coordinate ◽  
Special Solutions

We consider the classical motion of a point particle whose Lagrangian involves not only the usual arc length, but also the extrinsic curvature associated with its trajectory. This Lagrangian is independent of the parameterization used to characterize the trajectory; by choosing this parameter to be the time coordinate associated with the position of the particle in space-time, we obtain a Lagrangian dependent on the position, velocity, and acceleration of the particle in a co-moving frame. Some special solutions to the Hamiltonian equations of motion are presented for the case of the free particle and for a particle moving in a Coulomb field.

scholarly journals Solving Equations of Motion by Using Monte Carlo Metropolis: Novel Method Via Random Paths Sampling and the Maximum Caliber Principle

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 916
Author(s):  
Diego González Diaz ◽  
Sergio Davis ◽  
Sergio Curilef
Keyword(s):  
Monte Carlo ◽  
Energy State ◽  
Equations Of Motion ◽  
Free Particle ◽  
Classical Mechanics ◽  
Canonical System ◽  
Path Space ◽  
Lagrange Equations ◽  
Solving Equations ◽  
Novel Method

A permanent challenge in physics and other disciplines is to solve Euler–Lagrange equations. Thereby, a beneficial investigation is to continue searching for new procedures to perform this task. A novel Monte Carlo Metropolis framework is presented for solving the equations of motion in Lagrangian systems. The implementation lies in sampling the path space with a probability functional obtained by using the maximum caliber principle. Free particle and harmonic oscillator problems are numerically implemented by sampling the path space for a given action by using Monte Carlo simulations. The average path converges to the solution of the equation of motion from classical mechanics, analogously as a canonical system is sampled for a given energy by computing the average state, finding the least energy state. Thus, this procedure can be general enough to solve other differential equations in physics and a useful tool to calculate the time-dependent properties of dynamical systems in order to understand the non-equilibrium behavior of statistical mechanical systems.

scholarly journals Relativistic Rotation of the Rigid Body in the Rodrigues – Hamilton Parameters: Lagrange Function and Equations of Motion

2018 ◽  
Vol 53 (3) ◽  
pp. 89-115
Author(s):  
V.V. Pashkevich ◽  
G.I. Eroshkin
Keyword(s):  
General Relativity ◽  
Differential Equations ◽  
Rigid Body ◽  
Equations Of Motion ◽  
Lagrange Function ◽  
Riemann Space ◽  
Body Rotation ◽  
Rigid Body Rotation ◽  
Metric Properties ◽  
Relativistic Approximation

Abstract The main purposes of this research are to obtain Lagrange function for the relativistic rotation of the rigid body, which is generated by metric properties of Riemann space of general relativity and to derive the differential equations, determining the rigid body rotation in the terms of the Rodrigues - Hamilton parameters. The Lagrange function for the relativistic rotation of the rigid body is derived from the Lagrange function of the nonrotation point of masses system in the relativistic approximation.

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