欧几里德对称Hamilton系统轴对称相对平衡点的稳定性转移
Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems
摘要：
在非紧对称性的存在下，相对平衡点在动量保持扰动下的稳定性通常并不意味着在动量变化扰动下的鲁棒稳定性。对于轴对称相对平衡的哈密顿系统与欧几里得对称性，我们调查不同的机制的稳定性：稳定的能量动量限制，KAM，Nekhoroshev稳定性，我们解释这些之间的过渡。我们将我们的结果应用到Kirchhoff模型的轴对称水下航行器的运动，我们数值研究耗散引起的不稳定性KAM稳定的相对平衡这个系统。
英文摘要：
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.
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