Spin stabilization is a commonly used form of passive attitude control for spacecraft. The use of ball-in-tube dampers has been studied extensively for oblate spacecraft. It is widely known from classic rigid-body dynamics that, in the presence of energy dissipation, pure spin is stable only when performed about the axis associated with the maximum central principal moment of inertia. In this study, the Routh–Hurwitz criterion is used to obtain modifications to the classic rule for asymptotic stability of the major axis spin for two configurations, in which the tube is either parallel to or orthogonal to the spacecraft spin axis. A graphical comparison of the linear stability regions, which does not appear elsewhere in the literature, is presented for the two configurations. It is evident from the linear stability diagram that the conditions required for stability are stricter for a nutation damper than for a precession damper. The stability boundaries are subsequently confirmed with numerical solutions of the nonlinear equations of motion.

自旋稳定是航天器被动姿态控制的一种常用形式。对于扁球形航天器，已经广泛研究了球管阻尼器的使用。从经典刚体动力学众所周知，在存在能量耗散的情况下，仅当绕与最大中心主惯性矩相关的轴执行纯旋转时，纯旋转才会稳定。在这项研究中，使用Routh–Hurwitz准则对两种构造的主轴自旋的渐近稳定性的经典规则进行了修改，其中管平行于或正交于航天器自旋轴。对于这两种配置，给出了线性稳定性区域的图形比较，这在文献中没有出现。从线性稳定性图可以明显看出，螺母阻尼器的稳定性要求比进动阻尼器的稳定性要严格。随后通过非线性运动方程的数值解确定稳定性边界。