摘要
在位形空间中研究分数阶奇异系统的Lie对称性及其守恒量。给出分数因子法的分数阶导数定义,利用微分变分原理和Routh方法推导出外含Chetaev型非完整约束的奇异保守系统的运动微分方程;进一步研究在无限小群变换下系统Lie对称性的确定方程、限制方程和附加限制方程;根据对称性与守恒量之间的联系,构造规范生成函数满足的结构方程,进而得到一阶非完整分数阶奇异系统守恒量形式;最后举例说明方法的应用。结果表明,在外在非完整约束与奇异性导致的内在约束相容性基础上,利用分数因子法研究奇异系统得到的有关结论与经典整数阶约束力学系统具有高度的自然一致性,且简便和准确。
This paper studies Lie symmetries and conserved quantities of fractional singular systems in a square space, and gives a fractional derivative definition of fractional factor method. The differential equa-tions of motion for a singular conservative system with Chetaev type nonholonomic constraints are derived by using the differential variational principle and the Routh method. Furthermore, the determination equa-tions, the Limiting Equations and the additional Limiting Equations for the Lie symmetry of the system are studied under the infinitesimal group transformation. According to the relation between symmetry and ener-gy conservation, this paper constructs the structure equation generating functions, and then gets the energy conservation form of the nonholonomic fractional singular systems. Finally, an example is given to illustrate the application of the method. The results show that based on the internal constraint compatibility caused by the external nonholonomic constraints and singularity, relevant conclusions and the classical integer or-der constrained mechanical system obtained by fractional factor method of singular systems are of high nat-ural consistency, convenience and accuracy.
出处
《南通职业大学学报》
2017年第3期55-59,共5页
Journal of Nantong Vocational University
基金
国家自然科学基金项目(11472247)
关键词
分数因子
奇异系统
非完整
LIE对称
守恒量
fractional factor
singular system
nonholonomic
Lie symmetry
conserved quantity
