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1. Aerodynamic-Dynamic Interactions and Multi-Body Formulation of Flapping Wing Dynamics: Part II - Trim and Stability Analysis

   Hassan, Ahmed; Taha, Haithem (January 2017, AIAA Guidance, Navigation, and Control Conference)

   Flapping ight dynamics constitutes a multi-body, nonlinear, time-varying system. The two major simplifying assumptions in the analysis of apping ight stability are neglecting the wing inertial eects and averaging the dynamics over the apping cycle. The challenges resulting from relaxing these assumptions naturally invoke the geometric control theory as an appropriate analysis tool. In this work, a reduced-order model (extracted from the full model derived in the rst part of this work) for the longitudinal apping ight dynamics near hover is considered and represented in a geometric control framework. Then, combining tools from geometric control theory and averaging, the full dynamic stability as well as balance analyses of hovering insects are performed. 

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2. A combined Averaging-Shooting Approach for the Trim Analysis of Hovering Insects/Flapping-Wing Micro-Air-Vehicles

   Hassan, Ahmed; Taha, Haithem (January 2017, AIAA Guidance, Navigation, and Control Conference)

   Because of the wing oscillatory motion with respect to the body, the ight dynam- ics of biological yers as well as their man-made mimetic vehicles, apping-wing micro- air-vehicles (FWMAVs), are typically represented by multi-body, nonlinear time-periodic (NLTP) system models whose balance and stability analyses are quite challenging. In this work, we consider a NLTP system model for a two-degree-of-freedom FWMAV that is con ned to move along vertical rails. We combine tools from chronological calculus, geo- metric control, and averaging to provide a mathematically rigorous analysis for the balance of FWMAVs at hover; that is, relaxing the single-body and direct averaging assumptions that are commonly adopted in analyzing balance and stability of FWMAVs and insects. We also use optimized shooting to numerically capture the resulting periodic orbit and verify the obtained results. Finally, we provide a combined averaging-shooting approach for the balance and stability analysis of NLTP systems that (i) unlike typical shooting methods, does not require an initial guess; (ii) provides more accurate results than the analytical av- eraging approaches, hence relaxing the need for intractable high-order averaged dynamics; and (iii) allows a deeper scrutiny of the system dynamics, in contrast to numerical shooting methods. 

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

   https://doi.org/10.1007/s00332-018-9520-8  

   Hassan, Ahmed M.; Taha, Haithem E. (November 2018, Journal of Nonlinear Science)

   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 microair- 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 stabilizationmechanism 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. 

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4. Vibrational Control in Flapping-Wing Micro-Air-Vehicles

   Taha, H; Kiani, M; Navarro, J (June 2018, American Control Conference)

   Flapping-Wing Micro-Air-Vehicles (FWMAVs) are bio-inspired air vehicles that mimic insect and bird flight. The dynamic behavior of these systems is typically described by a multi-body, multi-time-scale, nonlinear, time-varying dynamical system. Interestingly, this rich dynamics lead to unconventional stabilization mechanisms whose study essentially necessitates a mathematically rigorous analysis. In this paper, we use higherorder averaging, which is based on chronological calculus, to show that insects and their man-made counterparts (FWMAVs) exploit vibrational control to stabilize their body pitching angle. Such an unconventional stabilization cannot be captured by direct averaging. We also experimentally demonstrate such a phenomenon by constructing an experimental setup that allows for two degrees of freedom for the body; forward motion and pitching motion. We measure the response of the body pitching angle using a digital camera and an image processing algorithm at different flapping frequencies. It is found that there is a flapping frequency threshold beyond which the body pitching response is naturally (without feedback) stabilized, which conforms with the vibrational control concept. Moreover, we also construct a replica of the experimental setup with the FWMAV being replaced by a propeller revolving at constant speed, which results in a constant aerodynamic force, leaving no room for vibrational control. The response of the propellersetup is unstable at all frequencies, which also corroborates the fact that the observed stabilization of the FWMAV-setup at high frequencies is a vibrational stabilization phenomenon. 

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5. Effects of body shape on aerodynamic performance and wake structures in snake-like gliding

   Gong, Y. (January 2022, AIAA)

   Flying snakes are the only snakes on Earth capable of aerial gliding, taking advantage of fluid dynamic principles to leap from point to point among the trees. During their gliding, the locomotion of aerial undulation is observed. We hypothesize that this locomotion and its associated unsteady vortex dynamics are critical to their aerodynamic performance. However, there is a lack of detailed three-dimensional flow field information around the snake body in gliding due to the difficulties in experimental flow visualizations of live animals. In this study, a computation fluid dynamics (CFD) study has been conducted to study the fluid dynamics of a snake-like gliding. A mathematical equation describing the horizontal undulation motion was applied for constructing snake-like 3D computational models and a series of flow simulations were conducted. An immersed-boundary-method (IBM)-based direct numerical simulation (DNS) flow solver along with adaptive mesh refinement (AMR) was used in the simulation. Specifically, different head positions, corresponding to different horizontal wave shapes and their effect on aerodynamic performance, flow field and wake structures behind the body will be studied. In addition, the dynamic undulating motion is introduced in the model and a CFD simulation is also conducted. Results from this study are expected to bring a step stone to understanding snake-inspired locomotion. 

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