Stability of Equilibria for the so(4) Free Rigid Body
Stability of Equilibria for the so(4) Free Rigid Body
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DOI：
10.1007/s00332-011-9113-2
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发表时间：
2012-04-01
影响因子：
3
通讯作者：
Turhan, Murat
中科院分区：
文献类型：
--
作者：
Birtea, Petre;Casu, Ioan;Turhan, Murat
6(4)刚体动力学的利泊松动力学的所有一般平衡的稳定性是完全确定的。证明了对于广义刚体，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so(4)的情况下，有三个坐标型Cartan子代数，它们与一个正则伴随轨道相交得到三个Weyl群平衡轨道。这些坐标型Cartan子代数类似于式(3)中经典刚体的三轴平衡。除了这些坐标型的卡坦均衡还有其他的曲线均衡。
The stability for all generic equilibria of the Lie-Poisson dynamics of the 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 so(n) are equilibrium points for the rigid body dynamics. In the case of so(4) there are three coordinate type Cartan subalgebras whose intersection with a regular adjoint orbit gives 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 so(3). In addition to these coordinate type Cartan equilibria there are others that come in curves.