New methods to find solutions and analyze stability of equilibrium of nonholonomic mechanical systems
New methods to find solutions and analyze stability of equilibrium of nonholonomic mechanical systems
复制标题
寻找解和分析非完整机械系统平衡稳定性的新方法
DOI：
10.1007/s10409-018-0768-x
复制
发表时间：
2018-03
期刊：
影响因子：
--
通讯作者：
Mei FX
中科院分区：
文献类型：
--
作者：
Chen J;Guo YX;Mei FX
A large proportion of constrained mechanical systems result in nonlinear ordinary differential equations, for which it is quite difficult to find analytical solutions. The initial motions method proposed by Whittaker is effective to deal with such problems for various constrained mechanical systems, including the nonholonomic systems discussed in the first part of this paper, where in addition to differential equations of motion, nonholonomic constraints apply. The final equations of motion for these systems are obtained in the form of corresponding power series. Also, an alternative, direct method to determine the initial values of higher-order derivativesis proposed, being different from that of Whittaker. The second part of this work analyzes the stability of equilibrium of less complex, nonholonomic mechanical systems represented by gradient systems. We discuss the stability of equilibrium of such systems based on the properties of the gradient system. The advantage of this novel method is its avoidance of the difficulty of directly establishing Lyapunov functions aimed at such unsteady nonlinear systems. Finally, these theoretical considerations are illustrated through four examples.
登录
查看更多内容
DOI：
10.1088/1009-1963/12/10/303
发表时间：
2003-10
期刊：
Chinese Physics
影响因子：
--
作者：
Z. Yi;Feng-xiang Mei
通讯作者：
Z. Yi;Feng-xiang Mei
DOI：
10.1088/1674-1056/24/5/054501
发表时间：
2015-03
期刊：
Chin. Phys. B
影响因子：
--
作者：
Mei Fengxiang;Wu Huibin
通讯作者：
Wu Huibin
DOI：
10.1016/c2009-0-61160-0
发表时间：
2003
期刊：
--
影响因子：
--
作者：
M. Hirsch;S. Smale;R. Devaney
通讯作者：
M. Hirsch;S. Smale;R. Devaney
影响因子：
1.4
作者：
Yongxin Guo;M. Shang;F. Mei
通讯作者：
Yongxin Guo;M. Shang;F. Mei
DOI：
10.1002/zamm.201200011
发表时间：
2013-08
期刊：
ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
影响因子：
--
作者：
D. Zeković
通讯作者：
D. Zeković