The dynamical equation for triaxial elastic Earth rotation

The research on dynamical theory for whole Earth rotation commonly is based on hypothesis of rotary symmetry of the earth.In practice,the earth is an non rolling-symmetry ellipsoid.Thereby,the theoretical researches on triaxial Earth model are in accordance with the practical requirement.On the basis of the Liouville dynamical equation,a dynamical equation for triaxial elastic Earth rotation is presented by maintaining the product of square of polar motion with ellipticity and ignoring lesser magnitude for all parameter in deductive process.Two methods for resolving free wobble of triaxial elastic Earth,ellipse integral and ellipse function,are proposed.Finally,it indicated that if lesser magnitude is holded in the deductive process,there will be not analytic resolution for dynamical equation of rotation of the elastic earth model.And the linear resolution of the rolling-symmetry Earth rotation only is an especial case of triaxial Earth model in magnitude of polar motion,even there is not second free wobble in triaxial elastic Earth model.