Modal Interpretation of Time-Varying Eigenvectors of Morphing Aircraft

The flight dynamics of morphing aircraft must be analyzed to ensure shapechanging trajectories have the desired characteristics. The tools for describing flight dynamics of fixed-geometry aircraft are not valid for time-varying systems such as morphing aircraft. This paper introduces a method to relate the flight dynamics of morphing aircraft by interpreting a time-varying eigenvector in terms of flight modes. The time-varying eigenvector is actually defined through a decomposition of the state-transition matrix and thus describes an entire response through a morphing trajectory. A variable-sweep aircraft is analyzed to demonstrate the information that is obtained through this method and how the flight dynamics are altered by the time-varying morphing. I. Introduction Morphing provides an ability to alter the shape of an aircraft and thus the flight characteristics. Such morphing is particularly attractive for unpiloted air vehicles due to the relative flexibility in their wings. Also, biologically-inspired concepts for morphing are abundant. The flight dynamics of morphing aircraft have received somewhat less attention than the flight performance. In a sense, studies into flight performance consider the characteristics of steadystate morphing whereas studies into flight dynamics consider the characteristics of time-varying morphing. These flight dynamics are critical to understanding the relative coupling between states when maneuvering. The role of eigenvalues and eigenvectors in describing the flight dynamics is well understood for linear time-invariant aircraft. These parameters are directly computed from the state matrix and directly relate properties of the response. Essentially, every real-valued eigenvalue and associated eigenvector describes a divergence or convergence while every complex-conjugate pair of eigenvalues and associated eigenvectors describe an oscillatory mode. This relationship of the flight dynamics with the eigenvalues and eigenvectors results from the exponential solution that is known for the linear time-invariant dynamics. A notion of eigenvalues and eigenvectors is also defined for linear time-varying systems; however, they actually are computed by decomposing the state-transition matrix rather than the state matrix. This requirement notes that the linear time-varying dynamics do not have a closed-form solution so any decomposition of the response must retain the temporal information within the

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