A Trigger of Coupled Singularities
A Trigger of Coupled Singularities
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耦合奇点的触发因素
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
K. Hedrih
中科院分区：
文献类型：
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作者：
K. Hedrih
以一对耦合齿轮的非线性动力学为例，研究了相平面相图中耦合奇点和同宿轨道数为8的触发器的出现和消失现象。这一现象是伴随而来的失去局部唯一均衡位置稳定性的现象。对于一定条件下的广义情形，定义了非线性动力保守系统的耦合奇点触发器的出现定理，系统势能的一阶导数是两个不同周期函数的乘积，一个分支参数是导致这两个函数出现新根的原因。
By using example of nonlinear dynamics of a pair of coupled gears, the phenomenon of appearance and disappearance of a trigger of coupled singularities and homoclinic orbits in the form of number ‘eight’ in the phase portrait in the phase plane is investigated. That phenomenon is an accompanying phenomenon of loss of stability of the local unique equilibrium position. For a generalized case under certain conditions, a theorem of the appearance of a trigger of coupled singularities in a nonlinear dynamical conservative system, the first derivative of the system potential energy which is a product of two periodic functions with different periods, and one bifurcation parameter, which is the cause for the appearance of new roots of these two functions, is defined.