Nonlinear realizations, the orbit method and Kohn's theorem
  The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on phase space is identified and compared with the one obtained with the help of Eisenhart lift. 
K. Andrzejewski, J. Gonera, P. Kosinski
hep-th math-ph math.MP