对称磁约束刚体哈密顿相对平衡的稳定性
Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies
摘要：
这项工作研究的对称性，相关的动量映射，和相对平衡的一个机械系统组成的一个小的轴对称的磁性体偶极子在轴对称的外部磁场，另外还表现出镜像对称性，我们称之为“轨道”。利用能量-动量方法研究了一类赤道准轨道相对平衡态的非线性稳定性，给出了其$\mathbb{T}^2$稳定性的充分条件，完善了文献中已有的部分稳定性关系.这些稳定性的处方明确地写下来的一些字段参数，它可以用于稳定的解决方案的设计。我们提出了新的线性方法来确定不稳定区域的背景下，我们使用的相对平衡，得出结论的一些非线性稳定条件的尖锐性。
英文摘要：
This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axisymmetric external magnetic field that additionally exhibits a mirror symmetry; we call this system the ``orbitron". We study the nonlinear stability of a branch of equatorial quasiorbital relative equilibria using the energy-momentum method and we provide sufficient conditions for their $\mathbb{T}^2$--stability that complete partial stability relations already existing in the literature. These stability prescriptions are explicitly written down in terms of the some of the field parameters, which can be used in the design of stable solutions. We propose new linear methods to determine instability regions in the context of relative equilibria that we use to conclude the sharpness of some of the nonlinear stability conditions obtained.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
