On the longitudinal oscillation of an aeroplane in turbulent air

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説明

In the present paper the dynamical response of the longitudinal motion of an aeroplane in turbulent air is treated under the assumption of small deviation from steady flight and the gust of wind acting on the aeroplane is assumed to have a spectrum with a Gaussian white noise. The dynamical response of the motion of the plane was found to be quite similar to the response in a linear system of coupled oscillators excited by random inputs. Under the assumption of a stationary simple Markoffian process, the transition probability which governs the random motion of the aeroplane was obtained by the Fokker-Planck equation. The average values of the motion of the plane were given as functions of time and their long-time behavior was also investigated with the eigenfunction expansion of solution of the stochastic differential equation.

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