Based on governing equations of liquid deviated flow in a precessing liquid-filled cylinder,thebifurcation equation in functional space is derived by the linear solutions of liquid inertial wave and axialsecondary flow and linear stability analysis of steady secondary flow.

At this moment the inertial wave oscillation of liquid in cylinder coupling with the nutating frequency of cylinder, the cylinder will result in resonant instability.

Voltage increment inertial filter that can distinguish the sudden changes of voltage amplitude,can conquer the time delay problem of the conventional inertial filter,and ensure the creditability of filtered voltage waveform at the point of amplitude sudden change.

But there are only a few researches on the relationship between the movement of Meiyu rain-band and inertia-gravity wave.

A set of the interaction equations of inertial gravity waves in a dissipative atmosphere on the basis of the weak nonlinear theory is derived.

The breaking mechanism of UIIW (usual inertial internal waves) and NIIW (fine scale near inertial internal waves) caused by shear instability due to f~ effect is studied following Part Ⅱ.