分数阶动力学的分析力学方法及其应用  

ANALYTICAL MECHANICS METHOD OF FRACTIONAL DYNAMICS AND ITS APPLICATIONS

作　　者：罗绍凯[1] Luo Shaokai(Institute of Mathematical Mechanics and Mathematical Physics,Zhejiang Sci Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学数学力学与数学物理研究所

出　　处：《动力学与控制学报》2019年第5期432-438,共7页Journal of Dynamics and Control

摘　　要：综述我们在分数阶动力学分析力学方法的研究进展,包括:分数阶动力学系统的分析力学表示,构造分数阶动力学模型的分析力学方法,构造分数阶动力学模型团簇的分析力学方法,三类分数阶Lie群无限小变换方法,分数阶动力学系统的对称性、对称性摄动和共形不变性的分析力学方法,分数阶动力学系统的代数结构与Poisson积分的分析力学方法,构造分数阶动力学系统积分不变量的分析力学方法,分数阶动力学系统梯度表示的分析力学方法,分数阶动力学系统稳定性的分析力学方法,分数阶微分方程的分析力学方法等,介绍了对于物理学、力学、生物学、非线性科学等领域的10多种分数阶动力学模型的应用,并指出了若干进一步研究的问题.A concise review on analytical mechanics methods for fractional dynamics was presented.It mainly fo cused on the analytical mechanics representations of fractional dynamical systems,the analytical mechanics meth ods for constructing a fractional dynamical model and a family of fractional dynamical models,three types of frac tional infinitesimal transformation for Lie group,the analytical mechanics methods for symmetry,symmetrical per turbation,conformal invariance,algebraic structure,Poisson integral,integral invariant,gradient representation,stability of fractional dynamical systems,and the analytical mechanics method of fractional differential equations.The applications of more than 10 kinds of fractional dynamics models in physics,mechanics,biology and non lin ear science were introduced.It also pointed out some problems should be studied further in the future.

关 键 词：分数阶动力学 分析力学 分数阶动力学模型团簇 分数阶Lie 变换 对称性 对称性摄 动 共形不变性 代数结构 Poisson 积分 积分不变量 梯度表示 稳定性 

分 类 号：G63[文化科学—教育学]