Influence of inner core rotation and obliquity on the inner core wobble and the free inner core nutation

The inner core wobble and the free inner core nutation are studied. A simple Earth model is adopted to derive all the results analytically. As new results over earlier work, the formulas of the frequencies of these two modes taking into account of the rotation rate and the obliquity of the inner core relative to the mantle are obtained. The formula for the inner core wobble is also used to study the inner core rotation relative to the mantle under some other assumptions.