A System of n=3 Coupled Oscillators with Magnetic Terms: Symmetries and Integrals of Motion

Abstract

The properties of a system of n = 3 coupled oscillators with linear terms in the velocities (magnetic terms) depending in two parameters are studied. We proved the existence of a bi-Hamiltonian structure arising from a non-symplectic symmetry, as well the existence of master symmetries and additional integrals of motion (weak superintegrability) for certain particular values of the parameters.

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (2)

• Superintegrability with third order invariants in quantum and classical mechanics
• A simple way of making a Hamiltonian system into a bi-Hamiltonian one

Cited by in corpus (3)

• Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem
• Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system
• Noncommutative Kepler Dynamics: symmetry groups and bi-Hamiltonian structures