自由刚体动力学：广义与经典
The free rigid body dynamics: generalized versus classic
摘要：
本文分析了定义在实$K$ -反对称矩阵的李代数$\mathfrak{o}(K)$的对偶上的一般二次Hamilton系统的标准形，其中$K$是任意的$3\times 3$实对称矩阵.主要结果的一个推论是，任何一阶自治三维微分方程具有两个独立的二次运动常数，其中允许一个正/负定线性组合，是仿射等价于经典的“松弛”自由刚体动力学与线性控制.
英文摘要：
In this paper we analyze the normal forms of a general quadratic Hamiltonian system defined on the dual of the Lie algebra $\mathfrak{o}(K)$ of real $K$ - skew - symmetric matrices, where $K$ is an arbitrary $3\times 3$ real symmetric matrix. A consequence of the main results is that any first-order autonomous three-dimensional differential equation possessing two independent quadratic constants of motion which admits a positive/negative definite linear combination, is affinely equivalent to the classical "relaxed" free rigid body dynamics with linear controls.
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