可积的有矩阻尼刚性转子族
An integrable family of torqued, damped, rigid rotors
摘要：
对刚体转动的欧拉方程的阐述常常使人想到一个特殊阻尼系统的概念，它的能量耗散，而它的角动量大小在物体坐标系中是守恒的。试图明确地构建这样一个阻尼函数导致一个更一般的，但仍然是可积的，系统的三次方程的轨迹被限制在嵌套套的二次曲面在角动量空间。对于某些参数的选择，沿着最大和最小转动惯量轴的固定点线可以同时吸引。极限情况是能量守恒或角动量守恒的情况。平行杆力学，微磁学，粒子与有效质量进行了简要讨论。
英文摘要：
Expositions of the Euler equations for the rotation of a rigid body often invoke the idea of a specially damped system whose energy dissipates while its angular momentum magnitude is conserved in the body frame. An attempt to explicitly construct such a damping function leads to a more general, but still integrable, system of cubic equations whose trajectories are confined to nested sets of quadric surfaces in angular momentum space. For some choices of parameters, the lines of fixed points along both the largest and smallest moment of inertia axes can be simultaneously attracting. Limiting cases are those that conserve either the energy or the magnitude of the angular momentum. Parallels with rod mechanics, micromagnetics, and particles with effective mass are briefly discussed.
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