分数阶力学系统的正则变换理论

发布时间：2018-01-01 13:27

本文关键词：分数阶力学系统的正则变换理论　出处：《应用数学学报》2016年02期 　论文类型：期刊论文

【摘要】：应用分数阶模型可以更准确地描述复杂系统的力学与物理行为,随着分数阶微积分在科学和工程的诸多领域的成功应用,传统的分析力学理论和方法需要拓展到含有分数阶微积分的系统.变换是分析力学研究的一个重要手段.本文研究分数阶力学系统的变换理论.基于Cuputo分数阶导数的定义,定义力学系统的Lagrange函数和Hamilton函数,在H(o|¨)lder交换关系下建立了分数阶Hamilton原理,并由分数阶Hamilton原理通过变分运算导出分数阶Hamilton正则方程;建立了分数阶力学系统的正则变换理论,给出了四种基本形式的分数阶正则变换,并通过算例说明母函数在分数阶正则变换中的作用.
[Abstract]:Application of fractional order model can more accurately describe the physical and mechanical behavior of complex systems, with the successful application of fractional calculus in many fields of science and engineering, mechanical analysis of the traditional theories and methods need to be extended to systems with fractional calculus. The transformation is an important means to analyze the mechanics research. This paper studies the transformation theory the fractional mechanical system. The definition of Cuputo based on fractional order derivative, Lagrange function and Hamilton function definition of the mechanical system, the relationship between H (o|) was established under the fractional Hamilton lder exchange principle, and by the fractional variational principle by Hamilton arithmetic derived fractional Hamilton canonical equation; establish the theory of canonical transformation fraction order of the mechanical system, gives the fractional canonical transformation of four basic forms, and an example shows the generating function in the fractional canonical transformation in use.

【作者单位】：苏州科技大学土木工程学院;
【基金】：国家自然科学基金(No.10972151,11272227,11572212)资助项目
【分类号】：O172;O316
【正文快照】： 1引言分数阶微积分是一个古老而又新颖的主题.说它古老,是因为其历史可以追溯到300年前莱布尼茨(1695年,1697年)的猜测和欧拉(1730年)的工作,并逐步发展到现在.然而,直到1974年才出版了第一本关于分数阶微积分理论的专著W,并且在最近的几十年间分数阶微积分在物理学、力学、电

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