Abstract: Reinvestigation of the Earth rotation is of scientific significance since the principle moments of inertia of the Earth,A,B,C are not equivalent with each other,and they are time-dependent.Numerical calculations of Euler's dynamic equations are provided when the temporal nature of the moments of inertia is taken into account.The results show that there is a free wobble with a period of 304.5 days;the three components of the angular velocity increase and decrease periodically;the variations of A,B,C lead to complex fluctuations of the Euler period,and especially,ω3 has oscillation periods 22,14,8,4,2 and 1 years as well as even shorter periods.In another word,the decadal,annual and even shorter-period fluctuations of length of day are closely related with the variations of A,B,C.