Decadal free polar motion of triaxial Earth

By using the elliptic function solution, the exact rotation solution of triaxial Earth is provided as motion of couple periods with an image decadal period longitudinally and Chandler wobble as transverse wave. To obtain the evident function result, we had to treat with Euler rotation equations with three times separated polar motions. The image period means transverse wave modulation that appears as phase modulation and the phase time series of the free wobble show decadal variation. The decadal wobble causes frequency modulation for free polar motion. The decadal wobble has 14.6 yr period that is almost 73/6 times or about 12 times of 1.191 yr period for Chandler wobble so that subharmonic resonance takes place. Applying subharmonic resonance theory in non‐linear oscillations, the amplitude of polar motions excited by the decadal additional wobble is provided as about 8.2 times magnifying the excitation amplitude. The decadal wobble of amplitude about 13 mas excites the polar motion on the average amplitude of 132 mas in addition of an about 108 mas amplitude modulation, range in (24, 240). This amplitude variation is almost identical to the observed data series.