Some aspects of equilibria,bifurcation and catastrophe of the nonlinear inertial motions are discussed. It is suggested that a disturbed air parcel which is inertially stable in the traditional sense may attain a new position rather than return to its original location due to nonlinear effects controlled by the local forcing. The air parcel may also "leap" from one equilibrium position to another. The sudden change of motion states may be caused by the gradual variation of intensity or frequency of the local forcing. This can account for certain behavior of the "index cycle" in the atmosphere.