Free Euler Motion of the Triaxial Earth Based on Temporary Principal Moments of Inertia of the Earth

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.