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The formalism of the averaged Lagrangian has been extended and developed to evaluate the intensitydependent precessional rotation and wave number shift of an elliptically polarized electromagnetic wave in unmagnetized cold relativistic plasmas; the results are identical to those of Arons and Max (1974) and others. Moreover, the expression for two intensity-induced nonlinear modulation frequencies for both the right and left circular polarization components of the wave have been derived. The mathematical technique developed here may be useful in the study of other types of nonlinearly evolved rotational corrections for motions in fluids, and so the possibilities of broadening the scope of this formalism are discussed.

Method of Averaged Lagrangian for Precessional Rotation and Other Complementary Effects of Waves in Nonlinear Plasmas