三轴刚性地球自由旋转欧拉角变化数值模拟研究

Numerical Simulation on the Free Rotation of The Earth as a Triaxial Rigid Body

假定地球是一个三轴刚性体,在Euclid空间中做自由旋转。在设定主惯性矩A小于B小于C的情况下,求解欧拉运动方程,得到数值解。计算结果表明:地球在除了自转和自由进动之外,同时还存在着自由章动。章动角会随着时间做周期性变化。重点讨论的是章动角的变化。

The Earth is taken as a triaxial rigid body,which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are solved, and the numerical results are provided. Calculations show that,besides the selfrotation of the Earth and the free Euler procession of the Earth＇s rotation,there exists the free nutation：the nutation angle, the angle between the Earth＇s momentary rotation axis and the mean axis, changes with time, but periodically. The free nutation is especially investigated.