Differential-Geometric-Control Formulation of Flapping Flight Multi-body Dynamics

Flapping flight dynamics is quite an intricate problem that is typically represented by a multi-body, multi-scale, nonlinear, time-varying dynamical system. The unduly simple modeling and analysis of such dynamics in the literature has long obstructed the discovery of some of the fascinating mechani...

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Bibliographic Details
Published in:Journal of nonlinear science 2019-08, Vol.29 (4), p.1379-1417
Main Authors: Hassan, Ahmed M., Taha, Haithem E.
Format: Article
Language:English
Subjects:
Aerodynamic loads
Aerodynamics
Analysis
Animal behavior
Classical Mechanics
Differential geometry
Dynamic stability
Economic Theory/Quantitative Economics/Mathematical Methods
Flapping wings
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Modelling
Multiscale analysis
Pendulums
Rotating bodies
Stability analysis
Stiffness
Theoretical
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Summary:Flapping flight dynamics is quite an intricate problem that is typically represented by a multi-body, multi-scale, nonlinear, time-varying dynamical system. The unduly simple modeling and analysis of such dynamics in the literature has long obstructed the discovery of some of the fascinating mechanisms that these flapping-wing creatures possess. Neglecting the wing inertial effects and directly averaging the dynamics over the flapping cycle are two major simplifying assumptions that have been extensively used in the literature of flapping flight balance and stability analysis. By relaxing these assumptions and formulating the multi-body dynamics of flapping-wing micro-air-vehicles in a differential-geometric-control framework, we reveal a vibrational stabilization mechanism that greatly contributes to the body pitch stabilization. The discovered vibrational stabilization mechanism is induced by the interaction between the fast oscillatory aerodynamic loads on the wings and the relatively slow body motion. This stabilization mechanism provides an artificial stiffness (i.e., spring action) to the body rotation around its pitch axis. Such a spring action is similar to that of Kapitsa pendulum where the unstable inverted pendulum is stabilized through applying fast-enough periodic forcing. Such a phenomenon cannot be captured using the overly simplified modeling and analysis of flapping flight dynamics.
ISSN:0938-8974
1432-1467
DOI:10.1007/s00332-018-9520-8