7个月周期极移的非线性动力机制

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。

Theoretical Approach to Polar Motion of 7-month-period

Chao (1983) studied the 7-month-period wobble existing in polar motion. Hopfner andJochman (1984) discussed the so-called half-Chandler wobble. Kosek and Kotaszek attracted itsinstable 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.Sothey 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 AtmosphericExcitation 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 7month-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 dynamicalequation 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 becomesas 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 inprobability 0 other than is stationary on a mean in probability 1. This shows that there are someunknown action modulating the CW frequency. By model analysis,it can be seen that, if the frequency of Chandler wobble is modulated about 3 96 by visco-elastic deformation, the amplitude ofChandler 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 theparameter resonance model of Chandler wobble. One is the 7-month-period wobble and the other isa motion of double period about 28 months. The 7-month-period wobble will be evidently observedsince the stability condition is satisfied.The amplitude of the 7-month-period wobble is about22.89 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, subChandler of 7-month-period is obtained from the model.