基于时变地球主惯性矩的三轴地球的自由Euler运动

Free Euler Motion of the Triaxial Earth Based on Temporary Principal Moments of Inertia of the Earth

在时变地球主惯性矩情形,采用数值方法求解了自由Euler动力学方程和运动学方程。结果表明,地球存在周期约为304.5 d的自由章动;旋转速度的三个分量均出现周期性的增大和减小;地球主惯性矩A、B、C的时变性导致Euler周期产生复杂的波动,特别是ω3(自转速率)存在周期为22 a1、4 a、8 a4、a、2 a、周年以及更短周期的波动,这表明A、B、C的时变性导致了10 a尺度、周年以及更短周期的日长变化。

Reinvestigation of the Earth rotation is of scientific significance since the principle moments of inertia of the Earth, A, B, C are not equivalent with each other, and they are time-dependent. Numerical calculations of Euler＇s dynamic equations are provided when the temporal nature of the moments of inertia is taken into account. The results show that there is a free wobble with a period of 304. 5 days; the three components of the angular velocity increase and decrease periodically; the variations of A, B, C lead to complex fluctuations of the Euler period, and especially, ω3 has oscillation periods 22, 14, 8, 4, 2 and 1 years as well as even shorter periods. In another word, the decadal, annual and even shorter-period fluctuations of length of day are closely related with the variations of A, B, C.