In the current research literature, the Chandler wobble is described as an impulse response with a characteristic frequency determined by the earth's ellipticity.

> https://en.wikipedia.org/wiki/Chandler_wobble "The existence of Earth's free nutation was predicted by Isaac Newton in Corollaries 20 to 22 of Proposition 66, Book 1 of the Philosophiæ Naturalis Principia Mathematica, and by Leonhard Euler in 1765 as part of his studies of the dynamics of rotating bodies. Based on the known ellipticity of the Earth, Euler predicted that it would have a period of 305 days. Several astronomers searched for motions with this period, but none was found. Chandler's contribution was to look for motions at any possible period; once the Chandler wobble was observed, the difference between its period and the one predicted by Euler was explained by Simon Newcomb as being caused by the non-rigidity of the Earth. The full explanation for the period also involves the fluid nature of the Earth's core and oceans .. "

There is a factor known as the Q-value which describes the resonant "quality" of the impulse response, classically defined as the solution to a 2nd-order DiffEq. The higher the Q, the longer the oscillating response. The following figure shows the impulse and response for a fairly low Q-value. It's thought that the Chandler wobble Q-value is very high, as it doesn't seem to damp quickly.

![impulse](http://1.bp.blogspot.com/-hBm3S3Gfu3s/T9Ypvnvq_vI/AAAAAAAADxA/awZ12LAIl5Q/s400/singleImpulse-300.png)

In contrast, ocean tides are not described as a characteristic frequency but instead as a transfer function and a "steady-state" response due to the forcing frequency. The forcing frequency is in fact *carried through* from the input stimulus to the output response. In other words, the tidal frequency matches the rhythm of the lunar (and solar) orbital frequency. There may be a transient associated with the natural response but this eventually transitions into the steady-state through the ocean's damping filter as shown below:

![ss](http://www.physik.uzh.ch/local/teaching/SPI301/LV-2015-Help/common/GUID-F5E84855-0619-4990-9053-8ADC3DD2A83E-help-web.png)

This behavior is well known in engineering and science circles and explains why the recorded music you listen to is not a resonant squeal but an amplified (and phase-delayed) replica of the input bits.

So why does the Chandler wobble appear close to 433 days instead of the 305 days that Euler predicted? If there was a resonance close to 305 days, any forcing frequency would be amplified in proportion to how close it was to 305 (or larger in Newcomb's non-rigid earth model). Therefore, why can't the aliased draconic lunar forcing cycle of 432.76 days be responsible for the widely accepted Chandler wobble of 433 days?

This is the biannual geometry giving the driving conditions.

![pic](http://imageshack.com/a/img923/9858/ViIcq9.png)

And this is the strength of the draconic lunar pull at a sample of two times a year, computed according to the formula cos(2$\pi$/(13.6061/365.242)*t), where 13.6061 days is the lunar draconic fortnight or half the lunar draconic month.

![](http://imageshack.com/a/img922/1644/bI7uGZ.png)

Can count ~127 cycles in 150 years, which places it between 432 and 433 days, which is the Chandler wobble period.

Yet again Wikipedia explains it this way:

> "While it has to be maintained by changes in the mass distribution or angular momentum of the Earth's outer core, atmosphere, oceans, or crust (from earthquakes), for a long time the actual source was unclear, since no available motions seemed to be coherent with what was driving the wobble.

One promising theory for the source of the wobble was proposed in 2001 by Richard Gross at the Jet Propulsion Laboratory managed by the California Institute of Technology. He used angular momentum models of the atmosphere and the oceans in computer simulations to show that from 1985 to 1996, the Chandler wobble was excited by a combination of atmospheric and oceanic processes, with the dominant excitation mechanism being ocean‐bottom pressure fluctuations. Gross found that two-thirds of the "wobble" was caused by fluctuating pressure on the seabed, which, in turn, is caused by changes in the circulation of the oceans caused by variations in temperature, salinity, and wind. The remaining third is due to atmospheric fluctuations."

Like ENSO and QBO, there is actually no truly accepted model for the Chandler wobble behavior. The one I give here appears just as valid as any of the others. One can't definitely discount it because the lunar draconic period precisely matches the CW period. If it did't match then the hypothesis could be roundly rejected.

And the same goes for the QBO and ENSO models described herein. The aliased lunisolar models match the data nicely in each of those cases as well and so can't easily be rejected. That's why I have been hammering at these models for so long, as a unified theory of lunisolar geophysical forcing is so tantalizingly close -- one for the atmosphere (QBO), the ocean (ENSO), and for the earth itself (Chandler wobble). These three will then unify with the generally accepted theory for ocean tides.

> https://en.wikipedia.org/wiki/Chandler_wobble "The existence of Earth's free nutation was predicted by Isaac Newton in Corollaries 20 to 22 of Proposition 66, Book 1 of the Philosophiæ Naturalis Principia Mathematica, and by Leonhard Euler in 1765 as part of his studies of the dynamics of rotating bodies. Based on the known ellipticity of the Earth, Euler predicted that it would have a period of 305 days. Several astronomers searched for motions with this period, but none was found. Chandler's contribution was to look for motions at any possible period; once the Chandler wobble was observed, the difference between its period and the one predicted by Euler was explained by Simon Newcomb as being caused by the non-rigidity of the Earth. The full explanation for the period also involves the fluid nature of the Earth's core and oceans .. "

There is a factor known as the Q-value which describes the resonant "quality" of the impulse response, classically defined as the solution to a 2nd-order DiffEq. The higher the Q, the longer the oscillating response. The following figure shows the impulse and response for a fairly low Q-value. It's thought that the Chandler wobble Q-value is very high, as it doesn't seem to damp quickly.

![impulse](http://1.bp.blogspot.com/-hBm3S3Gfu3s/T9Ypvnvq_vI/AAAAAAAADxA/awZ12LAIl5Q/s400/singleImpulse-300.png)

In contrast, ocean tides are not described as a characteristic frequency but instead as a transfer function and a "steady-state" response due to the forcing frequency. The forcing frequency is in fact *carried through* from the input stimulus to the output response. In other words, the tidal frequency matches the rhythm of the lunar (and solar) orbital frequency. There may be a transient associated with the natural response but this eventually transitions into the steady-state through the ocean's damping filter as shown below:

![ss](http://www.physik.uzh.ch/local/teaching/SPI301/LV-2015-Help/common/GUID-F5E84855-0619-4990-9053-8ADC3DD2A83E-help-web.png)

This behavior is well known in engineering and science circles and explains why the recorded music you listen to is not a resonant squeal but an amplified (and phase-delayed) replica of the input bits.

So why does the Chandler wobble appear close to 433 days instead of the 305 days that Euler predicted? If there was a resonance close to 305 days, any forcing frequency would be amplified in proportion to how close it was to 305 (or larger in Newcomb's non-rigid earth model). Therefore, why can't the aliased draconic lunar forcing cycle of 432.76 days be responsible for the widely accepted Chandler wobble of 433 days?

This is the biannual geometry giving the driving conditions.

![pic](http://imageshack.com/a/img923/9858/ViIcq9.png)

And this is the strength of the draconic lunar pull at a sample of two times a year, computed according to the formula cos(2$\pi$/(13.6061/365.242)*t), where 13.6061 days is the lunar draconic fortnight or half the lunar draconic month.

![](http://imageshack.com/a/img922/1644/bI7uGZ.png)

Can count ~127 cycles in 150 years, which places it between 432 and 433 days, which is the Chandler wobble period.

Yet again Wikipedia explains it this way:

> "While it has to be maintained by changes in the mass distribution or angular momentum of the Earth's outer core, atmosphere, oceans, or crust (from earthquakes), for a long time the actual source was unclear, since no available motions seemed to be coherent with what was driving the wobble.

One promising theory for the source of the wobble was proposed in 2001 by Richard Gross at the Jet Propulsion Laboratory managed by the California Institute of Technology. He used angular momentum models of the atmosphere and the oceans in computer simulations to show that from 1985 to 1996, the Chandler wobble was excited by a combination of atmospheric and oceanic processes, with the dominant excitation mechanism being ocean‐bottom pressure fluctuations. Gross found that two-thirds of the "wobble" was caused by fluctuating pressure on the seabed, which, in turn, is caused by changes in the circulation of the oceans caused by variations in temperature, salinity, and wind. The remaining third is due to atmospheric fluctuations."

Like ENSO and QBO, there is actually no truly accepted model for the Chandler wobble behavior. The one I give here appears just as valid as any of the others. One can't definitely discount it because the lunar draconic period precisely matches the CW period. If it did't match then the hypothesis could be roundly rejected.

And the same goes for the QBO and ENSO models described herein. The aliased lunisolar models match the data nicely in each of those cases as well and so can't easily be rejected. That's why I have been hammering at these models for so long, as a unified theory of lunisolar geophysical forcing is so tantalizingly close -- one for the atmosphere (QBO), the ocean (ENSO), and for the earth itself (Chandler wobble). These three will then unify with the generally accepted theory for ocean tides.