本文引用格式:罗绍凯.分数阶动力学的分析力学方法及其应用[J].动力学与控制学报,2019,17(5):432~438;   Luo Shaokai.Analytical mechanics method of fractional dynamics and its applications[J].Journal of Dynamics and Control,2019,17(5):432-438. 分数阶动力学的分析力学方法及其应用    点此下载全文 罗绍凯 浙江理工大学 数学力学与数学物理研究所,杭州 310018 基金项目： DOI：10.6052/1672-6553-2019-063 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. 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 Analytical mechanics method of fractional dynamics and its applications    Download Fulltext Luo Shaokai Fund Project: Abstract: A concise review on analytical mechanics methods for fractional dynamics was presented. It mainly focused on the analytical mechanics representations of fractional dynamical systems, the analytical mechanics methods for constructing a fractional dynamical model and a family of fractional dynamical models, three types of fractional infinitesimal transformation for Lie group, the analytical mechanics methods for symmetry, symmetrical perturbation, 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 linear science were introduced. It also pointed out some problems should be studied further in the future. Keywords:fractional dynamics,analytical mechanics,a family of fractional dynamical models,fractional Lie transformation,symmetry,symmetrical perturbation,conformal invariance,algebraic structure,Poisson integral,integral invariant,gradient representation,stability 查看全文  查看/发表评论  下载PDF阅读器

 您是第3503594位访问者 版权所有:《动力学与控制学报》 地址：湖南省长沙市湖南大学逸夫楼203室　邮编：410082 E_mail: dlxykzxb@hnu.edu.cn 　电话：0731-88822722 本系统由北京勤云科技发展有限公司设计