Journal of Nonlinear Science

, Volume 29, Issue 4, pp 1379–1417 | Cite as

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

  • Ahmed M. HassanEmail author
  • Haithem E. Taha


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.


Differential-geometric-control Flapping flight Time-periodic systems Vibrational stabilization Multi-body dynamic 

Mathematics Subject Classification

53Z05 93D99 34H15 76G25 



The authors gratefully acknowledge the support of the National Science Foundation Grant CMMI-1709746.


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Authors and Affiliations

  1. 1.Mechanical and Aerospace EngineeringUniversity of CaliforniaIrvineUSA
  2. 2.Henry Samueli Career Development Chair, Mechanical and Aerospace EngineeringUniversity of CaliforniaIrvineUSA

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