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首页> 外文期刊>Journal of aerospace engineering >Stability of Nonclassical Relative Equilibria of a Rigid Body in a J(2) Gravity Field
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Stability of Nonclassical Relative Equilibria of a Rigid Body in a J(2) Gravity Field

机译：J（2）重力场中刚体的非经典相对平衡的稳定性

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摘要

The gravitationally coupled orbit-attitude dynamics of a rigid body in a J(2) gravity field is a generalization of the traditional point-mass J(2) problem to take into account the gravitational orbit-attitude coupling of the considered body. Linear and nonlinear stability of nonclassical relative equilibria in the coupled orbit-attitude dynamics are studied with geometric mechanics in the present paper. Conditions of stability are obtained through the linear system matrix and projected Hessian matrix by using the energy-Casimir method. Linear and nonlinear stability regions are plotted in a wide range of system parameters. It is found that the stability regions are similar to those of classical relative equilibria while, at the same time, some differences do exist. For example, in some cases, the linear stability region contains not only the two regions that are analogues of the Lagrange region and DeBra-Delp region, but also a small irregular region in the third quadrant. Same as the case of classical relative equilibria, the nonlinear stability region is the subset of the linear stability region in the first quadrant, which is the analogue of the Lagrange region. (C) 2016 American Society of Civil Engineers.
机译：刚体在J（2）重力场中的重力耦合轨道-姿态动力学是对传统点质量J（2）问题的推广，其中考虑了所考虑物体的重力-轨道-姿态耦合。本文利用几何力学研究了耦合轨道-高度动力学中非经典相对平衡的线性和非线性稳定性。通过线性系统矩阵和投影的Hessian矩阵，使用energy-Casimir方法获得稳定性条件。在广泛的系统参数中绘制了线性和非线性稳定性区域。发现稳定性区域与经典相对平衡的区域相似，但同时也存在一些差异。例如，在某些情况下，线性稳定性区域不仅包含两个类似拉格朗日区域和DeBra-Delp区域的区域，而且还包含第三象限中的一个小的不规则区域。与经典相对平衡的情况相同，非线性稳定区域是第一象限中线性稳定区域的子集，这是拉格朗日区域的类似物。 （C）2016年美国土木工程师学会。

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