This dissertation introduces a set of novel approaches in order to facilitate and enrich Volterra theory as a nonlinear approximation technique for constructing mathematical solutions from the governing relationships describing aircraft dynamic behavior. These approaches reconnect Volterra theory and flight mechanics research, which has not been addressed in the technical literature for over twenty years. Volterra theory is known to be viable in modeling weak nonlinearities, but is not particularly well suited for directly describing high performance aircraft dynamics. In order to overcome these obstacles and restrictions of Volterra theory, the global Piecewise Volterra Approach has been developed. This new approach decomposes a strong nonlinearity into weaker components in several sub-regions, which individually only require a low order truncated series. A novel Cause-and-Effect Analysis of these low order truncated series has also been developed. This new technique in turn allows system prediction before employing computer simulation, as well as decomposition of existing simulation results. For a computationally complex and large envelope airframe system, a Volterra Parameter-Varying Model Approach has also been developed as a systematically efficient approach to track the aircraft dynamic model and its response across a wide range of operating conditions. The analytical and numerical solutions based on the proposed methodology show the ability of Volterra theory to help predict, understand, and analyze nonlinear aircraft behavior beyond that attainable by linear theory, or more difficult to extract from nonlinear simulation, which in turn leads to a more efficient nonlinear preliminary design tool.
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