7个月周期极移的非线性动力机制

Theoretical Approach to Polar Motion of 7-month-period

从滞弹性阻尼形变摄动造成CW频率调制假设出发 ,对CW的共振激发模型加上了参数的时变调制 ,变成了参数共振模型。经正演计算发现 ,参数共振模型完全符合CW的实际 ,表明滞弹性阻尼形变摄动造成频率的 3%调制 ,进一步使得CW振幅调制可达 70 %以上。这一参数共振模型是一个非线性动力系统 ,在非线性情况下 ,运动将发生分岔 ,即多解。

Chao (1983) studied the 7_month_period wobble existing in polar motion.Hopfner and Jochman (1984) discussed the so_called half_Chandler wobble.Kosek and Kotaszek attracted its instable amplitude as about ±10mas from the IERS polar motion data.They also attracted the oscillation of the 7_month_period from Atmospheric Excitation Function by spectrum analysis.So they pointed out that the 7_month_period wobble should be excited by the 7_monthe_period oscillation of Atmospheric Excitation Function.However,the 7_month_period oscillation of Atmospheric Excitation Function has an amplitude of about 1×10 -8 rad around the equator.This angular momentum is properly about 2mas,quite less than the 7_month_period wobble.Whether it is the 7_month_period oscillation of Atmospheric Excitation Function that excites the 7_month_period wobble,or vice versa? In this paper,the 7_month_period wobble is solved from the nonlinear dynamical equation of polar motion introduced by the author in 1999. Starting with frequency modulation of Chandler wobble in the model developed by introduction of damping from visco_elastic deformation,the dynamical model of Chandler wobble becomes as resonance model with time_dependent parameter.By evolution calculation,the parameter resonance model is essentially identical with the reality of Chandler wobble.Observing the CW frequency time IERS data it can be seen that CW frequency time series states on the inherent value in probability 0 other than is stationary on a mean in probability 1.This shows that there are some unknown action modulating the CW frequency.By model analysis,it can be seen that,if the frequency of Chandler wobble is modulated about 3% by visco_elastic deformation,the amplitude of Chandler wobble will be modulated higher than 70%.On the other hand,in the nonlinear dynamical system of parameter resonance model,bifurcation may occur,i.e. multiple solutions exist in the parameter resonance model of Chandler wobble.One is the 7_month_period wobble and the other is a motion of double period about 28 months.The 7_month_period wobble will be evidently observed since the stability condition is satisfied.The amplitude of the 7_month_period wobble is about 22.89 mas in maximum,and averages 12.65 mas.Furthermore,the stability condition of the bifurcation solution is discussed.Only stable periodic solution can be observed.In this paper,sub_Chandler of 7_month_period is obtained from the model.