Characterization of periodic motions in aircraft lateral dynamics

Limit cycles in aicraft lateral dynamics are called wing rock. Wing rock prevention and/or control is an important objective for aircraft that need to fly and maneuver at moderate to high angles of attack, This requires a characterization of wing rock periodic motions, which is our aim. Normal and large-amplitude types of wing rock are distinguished. Onset of normal wing rock occurs at a Hopf bifurcation followed by limit cycle oscillations of gradually growing amplitude. Onset of large-amplitude wing rock is similar, but the limit cycles following the Hopf bifurcation show a jump to a large-amplitude oscillation at a periodic saddle-node bifurcation. Large-amplitude wing rock is shown to be the result of lateral-longitudinal coupling in conjunction with a resonance condition. A continuation algorithm is used to track periodic solutions with varying parameters and to locate bifurcation points. A strategy to avoid large-amplitude wing rock is indicated on the basis of the study.