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On Stationary Motions of the Generalized Kowalewski Gyrostat and Their Stability

机译:广义Kowalewski陀螺仪的平稳运动及其稳定性

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The stationary motions of the Kowalewski gyrostat in two constant force fields are studied. It is revealed that the equations of motion of the gyrostat have the families of permanent rotations when the force fields are parallel, and the families of equilibria when these fields have special directions. It is shown that all the found solutions belong to an intersection of two invariant manifolds of codimension 2. The analysis of stability in the Lyapunov sense for these solutions is conducted.
机译:研究了Kowalewski陀螺仪在两个恒定力场中的平稳运动。结果表明,当力场平行时,陀螺仪的运动方程具有永久旋转族,而当磁场具有特殊方向时,则具有平衡族。结果表明,所有找到的解都属于两个维余不变流形的交集。对这些解进行了李雅普诺夫意义上的稳定性分析。

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