An analytical model of a second order system is extended from a single-axis framework, to a multi-axis, multi-degree of freedom framework for a multiple input, multiple output system. This mathematical model is built from the variational approach of the Volterra series representation of nonlinear systems. The new representation describes the second order, oscillatory natural modes of a system, and shows how to organize the Volterra terms in intuitive ways. The constructed mathematical model aims to establish an organization of the Volterra kernels to allow for analytical cause and effect type analysis on system behavior.
To demonstrate the accuracy of the developed Volterra model, the model is applied to atmospheric flight dynamics. A numerical simulation of an F-16 aircraft was developed based on the experimental data collected at NASA Langley and is compared to the Volterra model. Both longitudinal and latitudinal aircraft dynamics are analyzed, and the results show that the Volterra model effectively tracks the numerical simulations and has less error than a more conventional linearized system. The results show that weak nonlinearities of a system are predicted based on this new model. The construction of the model allows for a more effective analysis to the cause and effect of the response. Individual responses of each nonlinear component are separated for analysis, and each component’s effects on the total system response are observed
