$\mathfrak{so}(4)$自由刚体平衡点的稳定性
Stability of equilibria for the $\mathfrak{so}(4)$ free rigid body
摘要：
完全确定了$\mathfrak{so}(4)$刚体动力学的Lie-Poisson动力学的所有一般平衡点的稳定性。证明了对于广义刚体，$\mathfrak{so}(n)$的某些Cartan子代数（称为坐标型）是刚体动力学的平衡点。在$\mathfrak{so}(4)$的情形下，存在三个坐标型Cartan子代数，它们与一个正则伴随轨道的交给出三个外尔群的平衡轨道.这些坐标型Cartan子代数是$\mathfrak{so}(3)$中经典刚体平衡点三轴的类似物。除了这些坐标类型的Cartan均衡，还有其他曲线类型的均衡。
英文摘要：
The stability for all generic equilibria of the Lie-Poisson dynamics of the $\mathfrak{so}(4)$ rigid body dynamics is completely determined. It is shown that for the generalized rigid body certain Cartan subalgebras (called of coordinate type) of $\mathfrak{so}(n)$ are equilibrium points for the rigid body dynamics. In the case of $\mathfrak{so}(4)$ there are three coordinate type Cartan subalgebras whose intersection with a regular adjoint orbit give three Weyl group orbits of equilibria. These coordinate type Cartan subalgebras are the analogues of the three axes of equilibria for the classical rigid body in $\mathfrak{so}(3)$. In addition to these coordinate type Cartan equilibria there are others that come in curves.
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