Abstract: A nonlinear dynamic model of Euler pole is established byusing the Lagrangian description method. Based on the simplifications of thenonlinear dynamic model, a nonlinear static model, a linear dynamic model anda simplified nonlinear dynamic method are obtained, respectively. Atruncation of spectra is used to analyze the local bifurcation of thelinear dynamic model. On the basis of the analysis on the steady state of thesimplified nonlinear dynamic method, the bifurcation condition isobtained. This study shows that a forked bifurcation exists in the simplifiednonlinear dynamic model.