The Gyro-Kinetic Approximation. An attempt at explaining the method   based on Darboux Algorithm and Lie Transform
  This Proceeding presents the method that allows us to get the Gyro-Kinetic Approximation of the Dynamical System satisfied by the trajectory of a particle submitted to a Strong Magnetic Field. The goal of the method is to build a change of coordinates in order to make the dynamic of two components of the trajectory to disappear. This change of coordinates is based on a Darboux mathematical Algorithm and on a Lie Transform 
Emmanuel Frenod (Lab-STICC, INRIA Lorraine, IECN, LSIIT, IRMA),   Mathieu Lutz (INRIA Lorraine, IECN, LSIIT, IRMA, IRMA)
math.FA math-ph math.MP math.SG physics.plasm-ph