Electromagnetic Analog of 3D Autonomous ODEs with Quadratic Nonlinearities

Abstract

It is shown that the general class of three-dimensional first-order ordinary differential equations with quadratic nonlinearities can be physically interpreted as the dynamics of a charged particle in an electromagnetic field, with a constant gradient B-field. The general class of equations is derived within the Lagrangian formalism of classical mechanics. As an application of this interpretation a new way of experimentally realizing the Lorenz chaotic attractors is proposed. The actual construction of such systems could be facilitated by existing magnetic resonance imaging technology, which already makes use of constant gradient fields, and may find applications in areas such as nuclear medicine and magnetic confinement fusion devices.