【摘要】 给出了一类二阶非线性保守系统周期轨道族与同异宿轨道显式表示的初等积分方法;同时指出:根据周期轨道族外围分界线环类型的不同,周期轨道族需由不同的Jacobian椭圆函数来表示并揭示了其中的原因.利用文中方法,通过变量替换,旋转以及积分因子等手段,可推导获得某些更复杂非线性系统周期轨道族与同异宿轨道的显式式.因此所得结果对于非线性(扰动)系统分支与混沌的研究有帮助.更多还原

【Abstract】 The elementary integration method for deriving the explicit representations of periodic orbits families and homoclinic and heteroclinic orbits in a second-order nonlinear conservative system is given.It is pointed out that,according to the different separatrixes of periodic orbits families,the different Jacobian elliptic functions should be used.The associated reasons are revealed.Utilizing the method in this paper,the explicit representations of periodic orbits families and homoclinic and heteroclinic orbits in some more complex nonlinear systems can be obtained through changes of variables, rotations and integral factors,etc.Thus,the results in this paper benefit the study of bifurcations and chaos in nonlinear systems under perturbations.更多还原