The intricate concept of inherent stabilization of a mono-wing aerial vehicle, as a Nonlinear Time-Periodic (NLTP) system is investigated in this research. Stability analysis has been performed based on the dynamic characteristics of the system by using the most appropriate approaches, including Floquet theory, averaging theory, and kinetic energy integration. To achieve stable flight performance, specifying the admissible range of the aerodynamic coefficients and system parameters has been proposed. Using Floquet analysis, the system has initially been linearized around the periodic orbit that was found by numerical techniques. The stability condition of the linear model has been studied by evaluating the eigenvalues of the Monodromy matrix. Instability of the orbit has also been determined owing to the eigenvalues-greater-than-one rule. In averaging approach, time averaging is conducted over the fast time scale, transforming the NLTP system into the Nonlinear Time-Invariant (NLTI) one. Here, the new system is linearized around the trim condition, where two natural modes have been identified. The stable mode indicates coupling between the components of the linear and angular velocities, and the unstable mode appears due to the coupling of the yaw angle, the downward velocity, and the yaw rate. Furthermore, the cause of undesirable dynamic behavior has been investigated using kinetic energy time-history data. The proposed mono-wing exhibits instability with initial design condition that necessitates optimization of aerodynamic coefficients and geometric and inertia parameters. It is shown that the inherent stability of such NLTP system can be significantly improved by careful alteration of these parameters to achieve an optimal design.

本研究调查了作为非线性时间周期 (NLTP) 系统的单翼飞行器固有稳定性的复杂概念。基于系统的动态特性，采用Floquet理论、平均理论和动能积分等最合适的方法进行了稳定性分析。为了实现稳定的飞行性能，提出了规定气动系数和系统参数的允许范围。使用 Floquet 分析，系统最初已围绕通过数值技术发现的周期轨道线性化。通过评估Monodromy矩阵的特征值研究了线性模型的稳定性条件。由于特征值大于一规则，还确定了轨道的不稳定性。在平均方法中，时间平均是在快速时间尺度上进行的，将 NLTP 系统转换为非线性时不变 (NLTI) 系统。在这里，新系统围绕调整条件进行了线性化，其中已识别出两种自然模式。稳定模式表示线速度和角速度分量之间的耦合，不稳定模式由于偏航角、向下速度和偏航率的耦合而出现。此外，已经使用动能时程数据研究了不良动态行为的原因。拟议的单翼飞机在初始设计条件下表现出不稳定性，需要优化空气动力系数以及几何和惯性参数。