Calibrated and decalibrated approximations of nonlinear dynamic systems

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• 作者：Andrew J. Sinclair
• 关键词：Coordinate transformations ; Analytic approximations ; Linear approximations
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：87
• 期：1
• 页码：281-290
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

The motion of a physical system can generally be described by multiple coordinate representations, which obey nonlinear equations of motion and are related by nonlinear transformations. Here, the equivalence of the linearized equations of motion, related through the linearized transformations, is demonstrated. This equivalence is used to develop a calibrated linearized solution for highly nonlinear coordinates that can provide greater accuracy than the traditional linearized solution. The calibration process computes an alternate initial condition which is propagated with the linearized equations, instead of the true initial condition. Additionally, the inverse of the calibration process is used to develop a decalibrated solution, which is a nonlinear analytic approximation.