This paper investigates the periodic attitude motion of a gyrostat spacecraft in weakly elliptical orbits, focusing on the derivation of approximate analytical solutions and their stability. Unlike circular orbits, which allow for three types of regular precession, elliptical orbits are limited to cylindrical precession. Notably, the research identifies stable periodic attitude motions with the period matching the orbital period near hyperbolic precession in weakly elliptical orbits. The approximate analytical solutions for these periodic motions are derived and validated through numerical simulations of the spacecraft's nonlinear attitude dynamics. Stability analysis reveals that non-resonant scenarios yield stable periodic attitude motions, while internal and combination resonances may induce instability. These findings provide valuable insights for the design of spacecraft systems, enhancing energy-efficient attitude control essential for long-duration missions and optimizing operational performance in various aerospace applications. By leveraging the natural stability of periodic motions in elliptical orbits, this approach has the potential to enhance control accuracy, reduce energy consumption, and extend mission lifespans.

中文翻译：

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弱椭圆轨道陀螺仪航天器周期性姿态运动的解析解和稳定性


本文研究了陀螺仪航天器在弱椭圆轨道上的周期性姿态运动，重点介绍了近似解析解的推导及其稳定性。与允许三种类型的规则进动的圆形轨道不同，椭圆轨道仅限于圆柱形进动。值得注意的是，该研究确定了稳定的周期性姿态运动，其周期与弱椭圆轨道上双曲线岁差附近的轨道周期相匹配。这些周期性运动的近似解析解是通过对航天器非线性姿态动力学的数值模拟来推导和验证的。稳定性分析表明，非共振场景会产生稳定的周期性姿态运动，而内部和组合共振可能会引起不稳定。这些发现为航天器系统的设计提供了有价值的见解，增强了对长期任务至关重要的节能姿态控制，并优化了各种航空航天应用的运行性能。通过利用椭圆轨道上周期性运动的自然稳定性，这种方法有可能提高控制精度、降低能耗并延长任务寿命。