Shen Wenbin 1,2) ; Chen Wei 1) ; Zhang Di 3) ; Wang Wenjun 4) ; and Liang Yiqiang 1)
1)Department of Geophysics, School of Geodesy and Geomatics, Wuhan University, Wuhan 4300792)The Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, School of Geodesy and Geomatics, Wuhan University, Wuhan 4300793)Department of Geodesy and Surveying Engineering, School of Geodesy and Geomatics,Wuhan University, Wuhan 430079\ 4)Key Laboratory of Geophysical Dynamics, Institute of Geodesy and Geophysics, CAS,Wuhan 430077[
Abstract Under the assumption that the Earth is a triaxial rigid body which is rotating freely in the Euclidian space, the elliptic integral solution of the Euler dynamic equation is provided, and then the numerical solutions of the Euler dynamic as well as kinetic equation are realized. The calculated results show that, besides the selfrotation of the Earth with the period about 24 h and the free Euler precession with the period 305 d, there exists a free nutation with the period about 305 d. In addition, the three Eulerian angular velocities accelerate in a half period and decelerate in another half period, keeping the magnitude of the total angular velocity constant, i.e., the rotational energy keeps invariant. Correspondingly, the length of day increases gradually in one half period and decreases gradually in another half period.
