Nonlinear Spiral Simulation of Chandler Wobble Orbit

The classical dynamics model of polar motion is linear and its solution is of elliptic orbit.But there are excitations and damping in Chandler wobble, since the excitation function is not very stable.The damping and excitation cannot be made both ends meet in each period, too.So Chandler wobble may not follow elliptic orbit, instead its orbit should be spiral.The real posit ion of CW shows ro tating in a broad area.Of course, may be Chandler wobble reserves energy lossless in long time.However, at least in limited observations,Chandler wobble does not possess close elliptic orbit.No other than the damping and excitation are balanceable, the orbit may be elliptic.In this paper, spiral mot ion equation of Chandler wobble is deduced from combination of displacement in tangent and radial direct ions.In fact, the frequency series of CW is not stable on the inherent frequency.There is difference between the real frequency and the inherent frequency.The difference must be caused by the in-stable ex citation.Considering that the CW complex amplitude may be represented by the vector sum of the tangent and radial components, the complex amplitude is written as the vector sum of two terms, one is the free sway and the other is the common action of excitation and damping.Spiral orbit of Chandler wobble is better solved and coefficients of logarithm spiral equation are at tracted empirically.The amplitude of CW logarithm spiral equation is provided as ±5.4% per period, here the plus represents spiraling-out and the minus spiraling-in. The average spiral displacement amplitude of each Chandler period is given 6.75 milliarcsecond (mas),meanwhile 20 mas to -30 mas in maximum.Since the logarithm spiral parameter is instable one, it can be used empirically.Applying the empirical logarithm spiral equations to deduce Chandler amplitude, the square error with respect to the observation amplitude is only 0.0275 mas.On the other hand, the time series of the spiral displacement of each Chandler period shows an irregular process.By this time series, the inherent free sway has been moved away and remain signal should be from the excitation function.The act ion of excitation may be attracted mo re easily from the spiral amplitude moving away the average ellipse of the ideal orbit of Chandler wobble.