西南交通大学学报2017，Vol.52Issue(5)：1015-1019,5.DOI:10.3969/j.issn.0258-2724.2017.05.024
一类转动系统中质点的不变环面运动存在性问题
Existence Problem of Invariant Torus Particle Motion in Rotating Nonlinear Dynamical Systems
摘要
Abstract
In order to study whether the invariant torus of integrable Hamiltonian systems is retained under small perturbations,we established the Hamiltonian equations in polar coordinates. Using the first integral of the energy conservation equation,the transformation of the second-order state variable from a system with two degrees of freedom into a system with a single degree of freedom was analysed. Secondly,based on the Kolmogorov-Arnold-Moser (KAM)theorem,the existence of invariant tori in the perturbed system was confirmed. Finally,numerical simulations were performed to elucidate the analysis. The results show that the time history curve of the system is periodic,the phase portrait is dense,and the Poincaré map is a closed curve. The system is quasi-periodic,and the invariant torus of the integrable Hamiltonian system is shown to still exist under small perturbations. Moreover,the closed curve Poincaré mapping corresponds to the KAM invariant closed curve.关键词
哈密顿系统/KAM理论/不变环面Key words
Hamiltonian system/KAM theory/invariant torus分类
数理科学引用本文复制引用
王璟,谢建华,乐源..一类转动系统中质点的不变环面运动存在性问题[J].西南交通大学学报,2017,52(5):1015-1019,5.基金项目
国家色然科学基金资助项目(11272268,11172246) （11272268,11172246）
