三轴弹性地球自转的动力学方程

The dynamical equation for triaxial elastic Earth rotation

整体地球自转动力学理论一般假设地球是旋转对称的,但实际上地球是一个非对称的旋转椭球体。因此,三轴地球自转的研究是符合现实的。本文在弹性地球自转Liouville方程的基础上,在推导过程中所有量保留到极移平方和椭率乘积量级而忽略其更小量级的情况下,给出了适用于地球自转研究的三轴弹性地球自转的动力学方程。同时也列出了求解三轴弹性地球自转自由摆动的两种方法,即椭圆积分方法和椭圆函数方法。最后指出,如果在推导过程中保留更小量级,则弹性地球模型的自转动力学方程无解析解;旋转对称地球自转的线性解是三轴地球模型在极移量级下的一种特例,且三轴弹性地球模型不可能出现第二自由摆动。

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 ease of tfiaxial Earth model in magnitude of polar motion, even there is not second free wobble in triaxial elastic Earth model.