Nonlinear mechanism for polar motion with period of 7 months: Fid-Bau Portal

Nonlinear mechanism for polar motion with period of 7 months

Wang, W.-J.

Abstract. The 7 month-period (sub-Chandler) wobble is considered with respect to the nonlinear dynamical equation of polar motion. Starting with the frequency modulation of Chandler wobble (CW) in the model developed by introduction of damping from perturbed visco-elastic deformation, the rotation equation of the CW becomes a resonance model with a time-dependent parameter. According to evolution calculation, the parameter resonance model is essentially identical to the reality of CW observations. If the frequency of CW is modulated about 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} by visco-elastic deformation, then the amplitude of CW will be modulated by greater than 70\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. On the other hand, bifurcation may occur according to the nonlinear dynamical system of the parameter resonance model, i.e. a pair of solutions splitting from the main CW. One is the 7-month-period wobble and the other is a motion with a period of about 28 months. Although the latter is very weak, the 7-month-period wobble will be observed as the stability condition is satisfied. The maximum amplitude is about 22.89 mas and the average 12.65 mas. This is identical to what is observed in reality.