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首页> 外文期刊>International journal of non-linear mechanics >Chaos analysis in attitude dynamics of a satellite with two flexible panels
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Chaos analysis in attitude dynamics of a satellite with two flexible panels

机译：具有两个柔性面板的卫星姿态动力学中的混沌分析

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摘要

We investigate chaos in attitude dynamics of a satellite consisting of a rigid body and two flexible panels. We use the assumed mode method for the vibration of the panels and attempt to find an appropriate methodology to define the internal perturbation due to the flexibility of the panels, followed by the derivation of the Hamiltonian of the system. A canonical transformation on the entire flexible satellite is then applied, reducing the dimensionality of the system by two. The new Hamiltonian will have 2N +1 degrees of freedom with only two main variables. These two variables are preserved, while the rest of the variables are approximated by explicit functions of time due to the rotation of the main body. This will lead to the proof of the existence of a chaotic behavior using the Melnikov Wiggins' method, which in turn produces an analytical relation for the width of chaotic layers. This relation provides a means to make a proper comparison of the analytical and numerical results. The results obtained indicate that this approach is useful in the analysis of the effect of the parameters on the chaotic motion of the satellite. The results also show that one or at most two mode shapes suffice to reveal the vibration behavior of the panels and the effect of the panels on the chaotic behavior of the satellite.
机译：我们研究由刚体和两个柔性面板组成的卫星的姿态动力学中的混乱。我们使用假定模式方法来控制面板的振动，并试图找到一种合适的方法来定义由于面板的灵活性而引起的内部扰动，然后推导系统的哈密顿量。然后，对整个柔性卫星进行规范转换，从而将系统的维数减少两倍。新的哈密顿量将具有2N +1个自由度，只有两个主要变量。这两个变量得以保留，而其余变量则由于主体的旋转而通过显式的时间函数近似。这将导致使用梅尔尼科夫·威金斯（Melnikov Wiggins）方法证明混沌行为的存在，进而产生混沌层宽度的解析关系。这种关系提供了一种方法，可以对分析结果和数值结果进行适当的比较。获得的结果表明，该方法可用于分析参数对卫星混沌运动的影响。结果还表明，一个或最多两个模态形状足以揭示面板的振动行为以及面板对卫星混沌行为的影响。

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