# ChandlerWobble
Mathematical Geoenergy treatment of Chandler wobble mechanism.
Both `cw.py` and `claude/cw_fit_offline.py` use the same mass-normalized
Newtonian model: a damped 432.3-day oscillator receives additive momentum
impulses every 0.5 years. Each impulse magnitude is the unit-RMS square of the
27.212221-day draconic sinusoid. The free response is propagated exactly between
impulses; no continuous forcing or state-dependent (parametric) kick is used.
The optional `--amp-step s` adds the inertia pulse's effect on the wobble itself:
whole-year events scale the state by 1+s and half-year events by 1/(1+s), an annual
amplitude modulation that produces the 1 -/+ CW sidebands seen in `cw.dat` (`s = 0.25`
matches their level). Raw IERS polar motion since 1973 shows those sidebands 6-100 times
weaker in amplitude, consistent with the default s = 0; the `cw.dat` excess comes from its
processing (see `docs/cw_data_tests.md` §2).
## Interactive Visualization
**[Launch Interactive Model →](https://pukpr.github.io/ChandlerWobble/)**
Self-contained browser-based visualization (`index.html`) of the lunisolar forcing Chandler wobble model fitting 1950–2024 data. Features:
- Time series of observed vs. modeled polar motion Y (dY/dt or raw)
- Amplitude spectrum (Hann-windowed DFT) with annotated 365d / 433d / 183d peaks
- Polar motion phase plane (X vs Y) colored by decade
- Interactive sliders for draconic period, Q factor, nodal envelope, and training window
- Full model derivation: T_alias = 365.242 / (T_y/(T_d/2) − 26) ≈ 432.77 days
To run locally, open `index.html` in any browser (requires internet for D3.js CDN).
## Documentation
[
](https://agupubs.onlinelibrary.wiley.com/doi/10.1002/9781119434351.ch13)
- [`ChandlerWobbleForcing.pdf`](https://github.com/pukpr/ChandlerWobble/blob/main/ChandlerWobbleForcing.pdf) (2021 blog post: [https://geoenergymath.com/2021/01/07/chandler-wobble-forcing/](https://geoenergymath.com/2021/01/07/chandler-wobble-forcing/))
- [`dialog.pdf`](https://github.com/pukpr/ChandlerWobble/blob/main/dialog.pdf) (includes reference derivation and implementation notes)
- The simulatiom generates a temporal behavior that reproduces spectral components observed in the Chandler wobble time time series, crucially certain sidebands that won't appear in the consensus model.
## Usage
Run the main simulation with the desired spectral estimator:
default FFT
```bash
python cw.py
```
---
Maximum Entropy Model (MEM) order 400
```bash
python cw.py --spectral-estimator mem --ar-order 400
```
---
complex z-domain autoregressive (AR-z) order 100
```bash
python3 .\cw.py --spectral-estimator arz --ar-order 100
```
