旋转容器中重粒子的Brouwer问题：波传播，离子阱和转子动力学
Brouwer's problem on a heavy particle in a rotating vessel: wave propagation, ion traps, and rotor dynamics
摘要：
布劳威尔在1918年认为稳定的重粒子在旋转的船只。这是第一次演示的旋转鞍陷阱，这是一个机械模拟四极粒子陷阱的潘宁和保罗。我们重新审视这一开创性的工作，以揭示其有趣的连接与经典转子动力学和流体动力学，稳定性理论的哈密顿和非保守系统，以及与晶体光学和原子物理学的现代作品。特别地，我们发现无阻尼Brouwer问题的稳定域的边界具有对应于四重零特征值的燕尾奇异性。在耗散和非保守位置力的存在下，在渐近稳定域的边界上存在一对Whitney伞。伞柄形成一个集合，其中系统的所有本征值都是纯虚的，尽管存在耗散和非保守的位置力。
英文摘要：
In 1918 Brouwer considered stability of a heavy particle in a rotating vessel. This was the first demonstration of a rotating saddle trap which is a mechanical analogue for quadrupole particle traps of Penning and Paul. We revisit this pioneering work in order to uncover its intriguing connections with classical rotor dynamics and fluid dynamics, stability theory of Hamiltonian and non-conservative systems as well as with the modern works on crystal optics and atomic physics. In particular, we find that the boundary of the stability domain of the undamped Brouwer's problem possesses the Swallowtail singularity corresponding to the quadruple zero eigenvalue. In the presence of dissipative and non-conservative positional forces there is a couple of Whitney umbrellas on the boundary of the asymptotic stability domain. The handles of the umbrellas form a set where all eigenvalues of the system are pure imaginary despite the presence of dissipative and non-conservative positional forces.
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