Equivalence of two independent calculations of the higher order guiding   center Lagrangian
  The difference between the guiding center phase-space Lagrangians derived in [J.W. Burby, J. Squire, and H. Qin, Phys. Plasmas {\bf 20}, 072105 (2013)] and [F.I. Parra, and I. Calvo, Plasma Phys. Control. Fusion {\bf 53}, 045001 (2011)] is due to a different definition of the guiding center coordinates. In this brief communication the difference between the guiding center coordinates is calculated explicitly. 
F.I. Parra, I. Calvo, J.W. Burby, J. Squire and H. Qin
physics.plasm-ph