Purely magnetic satellite attitude control is considered. Special reference motion is constructed which provides local controllability. The angular trajectory is found in the neighborhood of unstable gravity gradient torque equilibrium. Direct solution for the minimization of the quadratic cost function representing the deviation from the equilibrium is derived. Linear equality type constraint on the torque direction is imposed. This solution is compared to the one found by the particle swarm optimization.

中文翻译：

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学院交易记录“最小偏差磁控卫星角轨迹的封闭形式解决方案”

考虑纯磁卫星姿态控制。构建了提供局部可控性的特殊参考运动。在不稳定的重力梯度力矩平衡附近发现角轨迹。导出代表偏离平衡的二次代价函数的最小化的直接解。对扭矩方向施加线性等式约束。将此解决方案与粒子群优化找到的解决方案进行比较。