Abstract: Based on the bifurcation analysis and Catastrophe theory methodology(BACTM), the aircraft global dynamic stability in rapid rolling maneuver is studied in this paper . Based on the study of the bifurcation and Catastrophe behavior of an aircraft in rapid rolling maneuver entering from vertical symmetry flight plane, the status of rapid rolling maneuver entering from horizontal turn is discussed futher. A general analytic formula for determining the critical rolling rate is derived in the state-control space. It indicates that the Phillips critical rolling rate criterion is noly a special case of the general analytic formula developed in this paper

Key words: Bifurcation analysis and Catastrophe theory, dynamic stability, rolling maneuver