Slow dynamics via degenerate variational asymptotics
Slow dynamics via degenerate variational asymptotics
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DOI：
10.1098/rspa.2014.0460
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发表时间：
2014-10
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影响因子：
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通讯作者：
G. Gottwald;M. Oliver
中科院分区：
文献类型：
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作者：
G. Gottwald;M. Oliver
介绍了一类奇摄动常微分方程在强陀螺力极限下的退化变分渐近方法。这样的系统在两个不同的时间尺度上表现出动态。我们推导出近似方程的慢运动到任意阶通过适当变换坐标的拉格朗日量的渐近展开。我们证明了必要的近身份的变化的变量总是可以构造和解决方案的慢极限方程的阴影解决方案的完整的父模型在预期的顺序在一个有限的时间间隔。
We introduce the method of degenerate variational asymptotics for a class of singularly perturbed ordinary differential equations in the limit of strong gyroscopic forces. Such systems exhibit dynamics on two separate time scales. We derive approximate equations for the slow motion to arbitrary order through an asymptotic expansion of the Lagrangian in suitably transformed coordinates. We prove that the necessary near-identity change of variables can always be constructed and that solutions of the slow limit equations shadow solutions of the full parent model at the expected order over a finite interval of time.