月球是离地球最近的天体,是人类探索宇宙与生命起源的天然实验台。月球探测器轨道设计是促使人类拓展三体问题等非线性动力学与控制问题的积极因素。严格的地月对称自由返回轨道存在于圆型限制性三体问题中(Cycler Restricted 3 Body Pr...
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月球是离地球最近的天体,是人类探索宇宙与生命起源的天然实验台。月球探测器轨道设计是促使人类拓展三体问题等非线性动力学与控制问题的积极因素。严格的地月对称自由返回轨道存在于圆型限制性三体问题中(Cycler Restricted 3 Body Problem,CR3BP),指能从近地空间出发,绕月一次后返回地球附近,期间不需要任何轨道控制的轨道,该类轨道空间轨迹关于地月连线具有对称性。本文求解了地月对称自由返回轨道解集域及近月点参数极值特性,并进一步分析了轨迹偏差的谱稳定性。研究结论有利于进一步认识CR3BP模型下,地月对称自由返回轨道存在性和解集奇异性,也可对月球及月球以远深空探测任务轨道设计与方案制定提供参考。
The behaviors of system which alternate between Duffing oscillator and van der Pol oscillator are investigated to explore the influence of the switches on dynamical evolutions of *** related to the state and time are ...
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The behaviors of system which alternate between Duffing oscillator and van der Pol oscillator are investigated to explore the influence of the switches on dynamical evolutions of *** related to the state and time are introduced,upon which a typical switched model is *** map of the whole switched system is defined by suitable local sections and local maps,and the formal expression of its Jacobian matrix is *** location of the fixed point and associated Floquet multipliers are calculated,based on which two-parameter bifurcation sets of the switched system are obtained,dividing the parameter space into several regions corresponding to different types of *** is found that cascading of period-doubling bifurcations may lead the system to chaos,while fold bifurcations determine the transition between period-3 solution and chaotic movement.
The paper investigates the generation of complex bursting patterns in the Duffing oscillator with nonlinear time-delayed *** patterns,including symmetric fold-fold,Hopf/Hopf and fold-Hopf bursting are obtained in the ...
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The paper investigates the generation of complex bursting patterns in the Duffing oscillator with nonlinear time-delayed *** patterns,including symmetric fold-fold,Hopf/Hopf and fold-Hopf bursting are obtained in the delayed equation when the periodic forcing changes *** analyze the bifurcations and dynamics of the system by regarding the delayed feedback and the periodic forcing as *** conditions of fold bifurcation as well as Hopf bifurcation and the stability related to forcing and time delay are presented,which have an intrinsic effect on the occurrence and mechanism of certain bursting *** regimes of bursting depending on the magnitude of the time delay itself and the strength of time delayed coupling are *** shows that the dynamics of the bursters in the delayed system are quite different from those of the bursters without *** particular,the time delay can be used as a tuning parameter to modulate the dynamics of bursting corresponding to the different types of the ***,the delayed bursting behaviors are illustrated by some numerical simulations.
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