扰动拟可积系统的平衡搜索算法
Equilibrium search algorithm of a perturbed quasi-integrable system
摘要：
本文介绍并研究了一种能搜索到只存在强迫振动项的轨道所对应的初始条件的算法，即完全去掉自由振动或固有振动部分的算法。该算法基于J.Laskar的基频数值分析算法，用于识别自由和强迫振动，通过仔细选择初始条件，将前者从解中迭代去除。我们证明了算法的收敛性在适当的假设下，满足在哈密顿框架下，只要达朗贝尔特征成立。在这种情况下，对于极典型变量，我们还证明了该算法的二次收敛性。我们提供了一个相关的应用：强迫捕食问题。
英文摘要：
We hereby introduce and study an algorithm able to search for initial conditions corresponding to orbits presenting forced oscillations terms only, namely to completely remove the free or proper oscillating part. This algorithm is based on the Numerical Analysis of the Fundamental Frequencies algorithm by J. Laskar, for the identification of the free and forced oscillations, the former being iteratively removed from the solution by carefully choosing the initial conditions. We proved the convergence of the algorithm under suitable assumptions, satisfied in the Hamiltonian framework whenever the d'Alembert characteristic holds true. In this case, with polar canonical variables, we also proved that this algorithm converges quadratically. We provided a relevant application: the forced prey-predator problem.
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