An Algorithm for Autonomous Non-linear Dynamical Equations

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Abstract
Summary The method of Beecham and Titchener is extended to systems with n degrees of freedom and is shown to be a combination of the averaging principle and the method of variation of parameters. In this extended form, the method provides a powerful solution algorithm for non-linear problems such as those which arise in aircraft structural dynamics and aeroelasticity. The method is exemplified in application to a two-degree-of-freedom damped non-linear oscillator and to a binary (flexure-aileron) non-linear flutter system. The method is finally extended to non-linear differential equations in first-order form such as those which arise commonly in flight mechanics.

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