Abstract

The dynamics of a satellite moving in a central Newtonian force field in a circular orbit under the influence of aerodynamic and active damping torques depending on projections of the satellite’s angular velocity is studied. A method for determining all equilibrium positions (equilibrium orientations) of the satellite in the orbital coordinate system given the values of aerodynamic torque, damping coefficients, and the principal central moments of inertia is proposed. In the case when the axes of the coordinate system attached to the satellite coincide with the axes of the orbital coordinate system, necessary and sufficient conditions for the asymptotic stability of the corresponding zero equilibrium position are obtained using the Routh–Hurwitz criterion. The domains with satisfied asymptotic stability conditions for the zero equilibrium position are analyzed depending on various dimensionless parameters of the problem. The damping of spatial oscillations of the satellite is numerically studied for various values of aerodynamic torque and damping coefficients.

中文翻译：

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受主动阻尼转矩影响的气动姿态控制系统对卫星运动的数学模拟

摘要

研究了在空气动力学和主动阻尼转矩的影响下，取决于卫星角速度投影的，在圆形轨道上的牛顿力中心圆形轨道中运动的卫星的动力学。提出了一种在给定空气动力学扭矩，阻尼系数和主要中心惯性矩值的情况下确定卫星在轨道坐标系中所有平衡位置（平衡方向）的方法。当附属于卫星的坐标系的轴线与轨道坐标系的轴线重合时，使用劳斯-赫维兹准则可获得相应零平衡位置渐近稳定性的必要和充分条件。根据问题的各种无量纲参数，对零平衡位置具有满意渐近稳定性条件的域进行分析。对空气动力转矩和阻尼系数的各种值进行了数值研究，研究了卫星空间振荡的阻尼。