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It is well-known that an electric charge under a uniform magnetic field has abidimensional motion if its initial position and velocity are perpendicular tothis magnetic field. Although some constants of motion, as the energy andangular momentum, have been identified for this system, its features hideothers. In this work, we build generalizations of the angular momentum and theLaplace-Runge-Lenz vector and show that these vectors are constants of motion.Moreover, from them, we find four dynamically independent conserved qualities.

Constants of motion for the magnetic force: the angular momentum and the Laplace-Runge-Lenz vector