It is well-known that an electric charge under a uniform magnetic field has a
bidimensional motion if its initial position and velocity are perpendicular to
this magnetic field. Although some constants of motion, as the energy and
angular momentum, have been identified for this system, its features hide
others. In this work, we build generalizations of the angular momentum and the
Laplace-Runge-Lenz vector and show that these vectors are constants of motion.
Moreover, from them, we find four dynamically independent conserved qualities.
Description
Constants of motion for the magnetic force: the angular momentum and the
Laplace-Runge-Lenz vector
%0 Generic
%1 velascomartinez2013constants
%A Velasco-Martínez, D.
%A Ibarra-Sierra, V. G.
%A Sandoval-Santana, J. C.
%A Kunold, A.
%A Cardoso, J. L.
%D 2013
%K helix
%T Constants of motion for the magnetic force: the angular momentum and the
Laplace-Runge-Lenz vector
%U http://arxiv.org/abs/1310.2591
%X It is well-known that an electric charge under a uniform magnetic field has a
bidimensional motion if its initial position and velocity are perpendicular to
this magnetic field. Although some constants of motion, as the energy and
angular momentum, have been identified for this system, its features hide
others. In this work, we build generalizations of the angular momentum and the
Laplace-Runge-Lenz vector and show that these vectors are constants of motion.
Moreover, from them, we find four dynamically independent conserved qualities.
@misc{velascomartinez2013constants,
abstract = {It is well-known that an electric charge under a uniform magnetic field has a
bidimensional motion if its initial position and velocity are perpendicular to
this magnetic field. Although some constants of motion, as the energy and
angular momentum, have been identified for this system, its features hide
others. In this work, we build generalizations of the angular momentum and the
Laplace-Runge-Lenz vector and show that these vectors are constants of motion.
Moreover, from them, we find four dynamically independent conserved qualities.},
added-at = {2017-01-29T22:31:46.000+0100},
author = {Velasco-Martínez, D. and Ibarra-Sierra, V. G. and Sandoval-Santana, J. C. and Kunold, A. and Cardoso, J. L.},
biburl = {https://www.bibsonomy.org/bibtex/2e1eae67dc8a0d225f4ef608a1b8e7694/ofrost},
description = {Constants of motion for the magnetic force: the angular momentum and the
Laplace-Runge-Lenz vector},
interhash = {e2a71a3d29d293d11b66055745744ac2},
intrahash = {e1eae67dc8a0d225f4ef608a1b8e7694},
keywords = {helix},
note = {cite arxiv:1310.2591Comment: 4 pages, 1 figures},
timestamp = {2017-01-29T22:31:46.000+0100},
title = {Constants of motion for the magnetic force: the angular momentum and the
Laplace-Runge-Lenz vector},
url = {http://arxiv.org/abs/1310.2591},
year = 2013
}