Concepts and Methods of Helicopter Local Stability for Aggressive Maneuvers of Short Duration From Response Data Points
Final rept. 1 Aug 2006-30 Apr 2007
FLORIDA ATLANTIC UNIV BOCA RATON
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This STTR work presents an exploratory investigation of helicopter stability during unsteady maneuvers on the basis of the finite time Lyapunov exponentsFTLE, These maneuvers represent short duration dynamics that lasts long enough to stall the rotor but not long enough to reach a steady state, they also represent aggressive operations at the extremes of the flight envelope that often represent a design condition. The Floquet approach is not applicable because it requires a periodic orbit, nor is the Lyapunov-exponent approach, which requires long-time response histories. The Lyapunov exponent reduces to FTLE under asymptotic conditions and to the real part of the Floquet exponent for a periodic orbit. Since these aggressive maneuvers represent unsteady dynamics of short duration, the formulation exploits the largest FTLE to calculate the stability of the least stable mode from experimentally or numerically generated response data. It involves constructing a pseudo-state space by the method of delays, generating a series of Jacobian matrices, and then forming the product of these matrices to generate an Oseledec matrix and its eigenvalues. The ongoing research is still in a developmental stage it represents the first attempt toward developing a framework for treating the stability of aggressive, short duration maneuvers.
- Theoretical Mathematics