We found Lagrangian action which describes spinning particle on the base of
non-Grassmann vector and involves only one auxiliary variable. It provides the
right number of physical degrees of freedom and yields generalization of the
Frenkel and BMT equations to the case of an arbitrary electromagnetic field.
For a particle with anomalous magnetic moment, singularity in the relativistic
equations generally occurs at the speed different from the speed of light.
Detailed discussion of the ultra-relativistic motion is presented in the work:
A. A. Deriglazov and W. G. Ramirez, World-line geometry probed by fast spinning
particle, arXiv:1409.4756.Comment: 8 pages, close to published version: paragraph about
ultra-relativistic motion is extended, the detailed discussion of this point
is presented in arXiv:1409.475