NORMAL FORM METHODS FOR COMPLICATED PERIODIC SYSTEMS: A COMPLETE SOLUTION USING DIFFERENTIAL ALGEBRA AND LIE OPERATORS
NORMAL FORM METHODS FOR COMPLICATED PERIODIC SYSTEMS: A COMPLETE SOLUTION USING DIFFERENTIAL ALGEBRA AND LIE OPERATORS
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2009
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我们提出了两种类型的形式算法：逐阶算法和“超收敛”过程，将单周期映射转化为所谓的范式形式，显示映射的调和内容。该算法在阶数、参数数量和相空间维度上是任意的，并且涵盖了圆形机器动力学中发现的未扰动二次不变量的特征范围。范式和映射提取算法都已事实上，由于微分代数理论和软件，本文的工作是完全可行的。
We present two types of formal algorithms: an ordcr-by-order and a "superconvergent" pro~'edurc" hringing the one-period map into a so-called normal form, which displays the harmonic content of the map. The algorithm is arbitrary in order, number of parameters, and phase-space dimen~ions and covers the range of signatures of the unperturbed quadratic invariants found in cir(ular-machine dynamics. The normal form and the map-extraction algorithms have all been implemented using the differential-algebra software. In fact, the work of this paper is feasible in toto hccause of the differential-algebra theory and software.