Theoretical Approach to Polar Motion of 7-month-period

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.