循环约化方法 Cyclic Reduction
行波约化方法 traveling wave reduction approach ; traveling wave reduction method
中心流形约化方法 Centre Manifold Reduction Method
约化法方程式 derived normal equation ; reduced normal equation
约束最优化方法 constrained optimization method
无约束最优化方法 unconstrained optimization method
序列无约束最小化方法 Sequential Unconstrained Minimization Technique
无约束优化方法 unconstrained optimization method
Applying simplified method and multi-scale method, the coupling vibration of the in-plane and outplane is studied. And the in-plane and out-plane vibration couples can be discovered when the cable抯 parameters satisfy certain conditions.
利用约化方法、多尺度法对斜拉索面内和面外的耦合振动进行了分析，发现在参数满足一定条件时，面内和面外的振动就会发生耦合。
参考来源 - 斜拉索的非线性动力学分析Applying simplified method and multi-scale method, the coupling vibration of the in-plane and outplane is studied. And the in-plane and out-plane vibration couples can be discovered when the cable抯 parameters satisfy certain conditions.
利用约化方法、多尺度法对斜拉索面内和面外的耦合振动进行了分析，发现在参数满足一定条件时，面内和面外的振动就会发生耦合。
参考来源 - 斜拉索的非线性动力学分析·2,447,543篇论文数据，部分数据来源于NoteExpress
利用中心流形约化方法证明了霍普夫分歧解的稳定性。
By using the method of centre manifold, the stability of the Hopf bifurcations is also proven.
对于标量粒子，其质量的获得则主要通过推广的平群约化方法。
And the mass for scalar particles is mainly given by generalized reduction on trivial group.
这些约化方法在其可应用的系统类型上有一定的局限性，比如其不能应用于不 完整 约束系统等。
There are restrictions on what type of systems these techniques can be applied to, e. g. , these reduction techniques do not apply to systems that are nonholonomically constrained.
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