# Bifurcation Flight Dynamic Analysis of a Strake-Wing Micro Aerial Vehicle
## 7 Conclusions  
The article presents application examples of the theory of dynamical systems relative to studying the flight dynamic specifics of a micro aerial vehicle, constructed as a fixed-wing aircraft with a strike-wing. Such microdrons are characterized by high manoeuvrability and can fly with high, supercritical angles of attack. The bifurcation analysis shown in the article enabled identifying some of the numerous factors impacting the behaviour of a strike-wing MAV. More specifically, this analysis allowed to discover a number of stable attractors, associated with disturbances to the states of equilibrium. Compared with purely simulational studies, which require long-term computations leading to the disappearance of motion history transitions on weak attractors, creating bifurcation diagrams is much less computation-demanding. Furthermore, bifurcation diagrams show the fundamental structure of a dynamical system, hence they suggest, where and when the time domain simulation should be conducted in order to better explain the behaviour of a dynamical system (in this case, a micro aerial vehicle). Time domain simulations were presented as supplementary to bifurcation diagrams, in order to gain more clarity in terms of the nature of various attractor dynamics regimes. It was shown that an MAV was susceptible to steep spiral motion disturbances, induced by loss of stability in this flight range. Bifurcation analysis was also able to identify that elevator displacement aimed at recovery from a steep spiral glide can lead to an oscillating spin. Bifurcation diagram analysis indicates that the correct reaction is to restore elevator position to the value corresponding to balancing conditions in straight flight. The approach adopted in this article can be extended in several ways. Firstly, MAV behaviour in an open control loop can be further tested through expanding the parameter space in question; this can cover additional control signals, as well as combining the centre of gravity and various damage scenarios, which can be added to the model. Another potentially beneficial extension is the use of bifurcation methods to analyse micro aerial vehicle models expanded with closed control loops, including bifurcation matching that enables recovery from critical flight states. Figure 14: “Cobra” manoeuvre. Poincare maps. **Author Contributions:** Conceptualization, K.S. and A.Z. ; methodology, M.N. ; software, A.S.-M.; validation, K.S. and M.N. ; formal analysis, K.S., and A.Z. ; writing--original draft preparation, M.N. and K.S. ; writing--review and editing, K.S. ; visualization, A.S-M.; supervision, M.N., and A.Z. ; project administration, K.S. ; funding acquisition, M.N., and A.Z. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was partially supported by Air Force Institute of Technology by subsidy from financial resources for the maintenance and development of research potential, and the statutory funds of the Faculty Mechatronics of the Warsaw University of Technology granted for 2020/2021. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest. **Abbreviations**