标题： 关于欧几里得对称哈密顿系统的轴对称相对平衡的稳定性转变 显示英文标题

标题： Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems

摘要： 在非紧致对称性存在的条件下，相对平衡在动量保持扰动下的稳定性通常并不意味着在动量改变扰动下的鲁棒稳定性。 对于具有欧几里得对称性的哈密顿系统的轴对称相对平衡，我们研究了不同的稳定性机制：能量-动量限制稳定性、KAM稳定性和Nekhoroshev稳定性，并解释了这些稳定性之间的转变。 我们将我们的结果应用于Kirchhoff模型以描述轴对称水下航行器的运动，并数值研究了该系统中KAM稳定的相对平衡由于耗散引起的不稳定性。 显示英文摘要

摘要： In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of Hamiltonian systems with Euclidean symmetry, we investigate different mechanisms of stability: stability by energy-momentum confinement, KAM, and Nekhoroshev stability, and we explain the transitions between these. We apply our results to the Kirchhoff model for the motion of an axisymmetric underwater vehicle, and we numerically study dissipation induced instability of KAM stable relative equilibria for this system.