双框架控制力矩陀螺奇异性分析

针对双框架控制力矩陀螺群的奇异性问题,定义了框架坐标系;提出了显隐奇点的ε-δ定义,并对奇点进行了3种分类;将陀螺群的角动量在奇点进行了泰勒展开,并定义了空转的判定条件;分析了陀螺群陷入奇异与各角动量相互平行的关系;针对定常转速且角动量大小相等的不限定框架构型的陀螺群的奇点问题,给出了内奇点必是隐奇点的严格证明.通过三正交构型20°纬度圈的最小显奇点的实例验证了内奇点必是隐奇点的论点. 

Double gimbal control moment gyroscopes singularity analysis

Aimed at analyzing the singularity of double gimbal control moment gyroscopes(DGCMGs), a gimbal reference frame, an ε-δ definition of apparent and concealed singular points, three sorts of singular points, system momentum taylor series expanded formula at singular point and a determination of null motions were proposed. The relation between singularity of the system and parallelism of each gyroscope angular momentum was discussed. It was strictly proved that the DGCMGs with constant velocity and equal angular momentum and without limit of configuration, has the property that inside singular points must be concealed singular ones. The views above were examined through the numerical simulation of minimal apparent singular points of three orthogonal configuration’s 20° latitude circle.