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余弦定理

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Via the stochastic averaging method, the four-dimensional system is reduced to a two-dimensional one. Through the logarithmic polar transformation , and then Girsanov theorem and Feynmann-Kac formula, the backword differential operator is then obtained. By expanding the eigenfunctions as a Fourier cosine series, the approximate analytic expansion of the moment Lyapunov exponent is then obtained.

首先在经典二元机翼颤振方程加入随机激励,通过随机平均法,Girsanov定理和Feynmann-Kac公式得到关于矩Lyapunov指数的特征值问题,其次采用Fourier余弦级数对特征函数进行正交展开得到系统矩Lyapunov指数的近似解析式。

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