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What is Indicial Theory?

Nonlinear indicial theory [1,2] asserts that the response of a nonlinear system to an arbitrary input can be constructed by integrating a nonlinear functional which involves the knowledge of the time-dependent input and a kernel response. This kernel response is a characteristic of the system. Once the kernel is known, the response of the system to arbitrary input can always be calculated. The well-known linear equivalent of this kernel is the linear impulse response, which can be convolved with the input to predict the output of a linear system. Nonlinear indicial theory is a generalization of this concept. It can also be shown that the traditional Volterra-Wiener theory of nonlinear systems [3,4] constitutes a subset of nonlinear indicial theory.


[1] Tobak, M., Chapman, G. T., and Schiff, L. B., "Mathematical Modeling of the Aerodynamic Characteristics in Flight Dynamics," NASA TM 85880, 1984.

[2] Tobak, M. and Chapman, G. T., "Nonlinear Problems in Flight Dynamics Involving Aerodynamic Bifurcations," NASA TM 86706, 1985.

[3] Volterra, V., "Theory of Functionals and of Integral and Integro-Differential Equations," Dover Publications, Inc., New York, 1959.

[4] Wiener, N.: Response of a Non-Linear Device to Noise, Report No. 129, Radiation Laboratory, M.I.T., Cambridge, MA, Apr. 1942.

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