# Bifurcation Flight Dynamic Analysis of a Strake-Wing Micro Aerial Vehicle
###### Abstract  
Non-linear phenomena are particularly important in -flight dynamics of micro-class unmanned aerial vehicles. Susceptibility to atmospheric turbulence and high manoeuvrability of such aircraft under critical flight conditions cover non-linear aerodynamics and inertia coupling. The theory of dynamical systems provides methodology for studying systems of non-linear ordinary differential equations. The bifurcation theory forms part of this theory and deals with stability changes leading to qualitatively different system responses. These changes are called bifurcations. There is a number of papers, the authors of which applied the bifurcation theory for analysing aircraft flight dynamics. This article analyses the dynamics of critical micro aerial vehicle flight regimes. The flight dynamics under such conditions is highly non-linear, therefore the bifurcation theory can be applied in the course of the analysis. The application of the theory of dynamical systems enabled predicting the nature of micro aerial vehicle motion instability caused by bifurcations and analysing the post-bifurcation microdrone motion. This article presents the application of bifurcation analysis, complemented with time-domain simulations, to understand the open-loop dynamics of stake-wing micro aerial vehicle model by identifying the attractors of the dynamic system that manages upset behaviour. A number of factors have been identified to cause potential critical states, including non-oscillating spirals and oscillatory spins. The analysis shows that these spirals and spins are connected in a one-parameter space and that due to improper operation of the autopilot on the spiral, it is possible to enter the oscillatory spin. nonlinear dynamics of flight; bifurcation theory; micro aerial vehicles; strike-wing micro drones +
Footnote †: journal: Applied Sciences  
**Multi-dimensional systems**  
this case. There was a need to develop a new method for testing aircraft motion stability, which would enable studying its dynamic properties throughout the entire range of usable angles of attack and slip. In the second half of the 20 th century, researchers suggested a continuation method based on the bifurcation theory that enabled analysing dynamic properties of an aircraft, over a wide range of flight states. Articles on this matter, published in the 1970s include: [4,5]. The cited research work concerned the analysis of a fast inertial barrel roll and spin. Numerous studies devoted to the bifurcation analysis of aircraft flight dynamics and aerodynamics appeared in the 1970s, 80s and 90s. These include the AGARD report from 1985 [6], and many papers on the issues of non-stationary aerodynamics and non-linear dynamics of flight in the perspective of the dynamical system theory and the bifurcation theory: [7-14]. The dynamical system theory enabled a global analysis of a system of strongly non-linear ordinary differential equations describing the state of a dynamical system, and in this aspect it is a generalization of the aforementioned dynamic stability analysis involving a steady straight flight of an aircraft. The first step in this method is the assessment of quasi-steady state stability. The quasi-steady state is determined by equating the derivatives of state vector to zero and solving a system of non-linear algebraic equations. The local stability of a dynamical system can be assessed based on the [PERSON] [15] theorem. This stability is determined by the eigenvalues of a locally linearised equations of MAV flight dynamics. In our case, this system is linearized around the equilibrium position, [7-14]. If even one of eigenvalues has a positive real part, then the equilibrium position is unstable. It can be proved that if a linearized equation system is non-singular, then the steady state of a dynamical system is a continuous function of state parameters [15]. It can also be proved that steady states of differential equations describing an aircraft motion are continuous functions of rudder surface deflections [16].