三轴弹性地球自转的动力学方程

发布时间：2018-08-18 16:07

【摘要】：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。
[Abstract]:The theory of global earth rotation dynamics generally assumes that the earth is rotationally symmetric, but in fact the earth is an asymmetric rotating ellipsoid. Therefore, the study of the triaxial rotation of the earth is in line with the reality. In this paper, on the basis of the Liouville equation of the elastic earth rotation, when all the variables are retained to the order of magnitude of the polar shift square and the ellipticity product in the derivation process, the smaller order of magnitude is neglected. The dynamic equations of triaxial elastic earth rotation are given, which are suitable for the study of earth rotation. At the same time, two methods for solving the free swing of the rotation of the three-axis elastic earth are listed, that is, the elliptic integral method and the elliptic function method. Finally, it is pointed out that if a smaller order of magnitude is retained in the derivation, there is no analytical solution to the rotation dynamic equation of the elastic earth model, and the linear solution of the rotation of the rotational symmetric earth is a special case of the three-axis earth model under the order of polar shift. And the second free swing is not possible in the triaxial elastic earth model.
【作者单位】：河南理工大学测绘学院;
【基金】：河南省科技创新人才计划(094100510023) 地球空间环境与大地测量教育部重点实验室测绘基础研究基金(0702) 河南省基础与前沿研究项目(082300460140)
【分类号】：P183.31

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