完整系统的分数维梯度表示及其稳定性分析  

Fractional gradient representations and stability analysis of holonomic systems

作　　者：王嘉航[1,2] 顾玲 翟相华 WANG Jiahang;GU Ling;ZHAI Xianghua(School of Civil Engineering,SUST,Suzhou 215011,China;College of Civil and Transportation Engineering,Hohai University,Nanjing 210098,China)

机构地区：[1]苏州科技大学土木工程学院,江苏苏州215011 [2]河海大学土木与交通学院,江苏南京210098

出　　处：《苏州科技大学学报（自然科学版）》2021年第4期16-22,共7页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11972241);江苏省自然科学基金资助项目(BK20191454);苏州科技大学科研基金资助项目(XKZ2017005)。

摘　　要：研究完整系统的分数维梯度表示及其稳定性分析。首先,基于分数维梯度系统的定义和微分方程,研究准坐标下完整系统、相对运动力学系统和变质量完整系统成为α=2阶的分数维梯度系统的条件;其次,利用分数维梯度系统的性质研究相应系统的稳定性问题;最后,举例说明结果的应用。This paper studies the fractional gradient representations of the holonomic systems and analyzes their stability.Firstly,based on the definition and differential equation of the fractional gradient system,the conditions of making a holonomic system under quasi-coordinates,a dynamical system of the relative motion and a variable mass holonomic system be a fractional gradient system of order α=2 were explored respectively.Secondly,the stability of the corresponding system was discussed with the properties of the fractional gradient system.Finally,the examples were given to illustrate the application of the results.

关 键 词：完整系统 分数维梯度表示 稳定性 准坐标 相对运动 变质量 

分 类 号：O316[理学—一般力学与力学基础]