Multiple time-scales in nonlinear flight mechanics: diagnosis and modeling
Multiple time-scales in nonlinear flight mechanics: diagnosis and modeling
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DOI：
10.1016/j.amc.2004.06.015
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发表时间：
2005-05
期刊：
影响因子：
--
通讯作者：
K. Mease
中科院分区：
文献类型：
--
作者：
K. Mease
飞行动力学中通常存在不同的时间尺度，这为简化模拟、分析和设计的降阶建模创造了可能性。在开发降维模型方面取得了显著的成功；然而，在制导问题中通常必须处理的非线性动力学的情况下，还没有一种系统、可靠的手段来诊断不同的时间尺度和开发降维模型。针对非线性动力系统中的两种时间尺度行为，我们回顾了Fenichel对流的几何结构的刻画，以及他建立了与这种结构相适应的坐标的存在和性质的定理。如果没有适当的奇异摄动动力学模型，就很难直接构建适应的坐标。我们讨论了利用Lyapunov指数和向量来诊断两个时间尺度的行为，并确定相应的线性化动力学的切线空间结构。然后，线性化流动的结构可以转化为非线性流动的流形结构。我们简要地提到了使用Lyapunov向量来定位慢流形，并将该方法与现有的两种方法进行了对比。最短攀登时间问题提供了两个时间尺度行为的例子，并激发了讨论。
There are often disparate time-scales in the dynamics of flight, creating the potential for reduced-order modeling to simplify simulation, analysis and design. There have been notable successes in developing reduced-order models; however, in the case of nonlinear dynamics, which one must typically deal with in guidance problems, there has not been a systematic, reliable means of diagnosing disparate time-scales and developing reduced-order models. Focusing on two time-scale behavior in nonlinear dynamical systems, we recall Fenichel’s characterization of the geometric structure of the flow and his theorem establishing the existence and properties of coordinates adapted to this structure. Adapted coordinates are difficult to construct directly, without an appropriate singularly perturbed model of the dynamics. We discuss the use of Lyapunov exponents and vectors to diagnose two time-scale behavior and to determine the corresponding tangent space structure for the linearized dynamics. The structure of the linearized flow can then be translated into the manifold structure of the nonlinear flow. We briefly mention the use of Lyapunov vectors to locate a slow manifold and contrast this approach with two existing approaches. The minimum time to climb problem provides an example of two time-scale behavior and motivates the discussion.