用具有负定非对称矩阵的梯度系统构造稳定的广义Birkhoff系统

发布时间：2018-01-07 01:07

本文关键词：用具有负定非对称矩阵的梯度系统构造稳定的广义Birkhoff系统　出处：《力学学报》2017年01期 　论文类型：期刊论文

【摘要】：Birkhoff系统是一类比Hamilton系统更广泛的约束力学系统,可在原子与分子物理,强子物理中找到应用.非定常约束力学系统的稳定性研究是重要而又困难的课题,用构造Lyapunov函数的直接方法来研究稳定性问题有很大难度,其中如何构造Lyapunov函数是永远的开放问题.本文给出一种间接方法,即梯度系统方法.提出一类梯度系统,其矩阵是负定非对称的,这类梯度系统的解可以是稳定的或渐近稳定的.梯度系统特别适合用Lyapunov函数来研究,其中的函数V通常取为Lyapunov函数.列出广义Birkhoff系统的运动方程,广义Birkhoff系统是一类广泛约束力学系统.当其中的附加项取为零时,它成为Birkhoff系统,完整约束系统和非完整约束系统都可纳入该系统.给出广义Birkhoff系统的解可以是稳定的或渐近稳定的条件,进一步利用矩阵为负定非对称的梯度系统构造出一些解为稳定或渐近稳定的广义Birkhoff系统.该方法也适合其他约束力学系统.最后用算例说明结果的应用.
[Abstract]:Birkhoff system is a constrained mechanical system analog Hamilton system more widely, in atomic and molecular physics, hadron physics. To find the application of non stability of often constrained mechanical systems is an important and difficult task, by the direct method of constructing Lyapunov function to study the stability problem is very difficult, including how to construct Lyapunov function is an open problem forever. This paper presents a method of indirect methods, namely gradient system. A gradient system, the negative definite matrix is non symmetric, the gradient of the solution of the system can be stable or asymptotically stable. Lyapunov function is used to study especially for the gradient system, the function of V is usually taken for the Lyapunov function. The equations of motion of lists of generalized Birkhoff system and generalized Birkhoff system is a wide class of constrained mechanical systems. When the additional term is zero, it becomes a Birkhoff System, holonomic and nonholonomic constraints can be incorporated into the system. The system can be stable or asymptotically stable conditions for generalized Birkhoff system, further using matrix negative gradient system constructed for stable or asymptotically stable solutions of the generalized Birkhoff system non symmetric. This method is also suitable for other mechanical constraints the application of system. At last an example is presented to illustrate the results.

【作者单位】：商丘师范学院物理与电气信息学院;苏州科技大学数理学院;北京理工大学宇航学院;
【基金】：国家自然科学基金资助项目(11372169,11572034,11272050)
【分类号】：O316
【正文快照】： 引言 1927年Birkhoff在其名著《动力系统》中提出了一类新型的积分变分原理和运动微分方程[1],被分别称为Pfaff-Birkhoff原理和Birkhoff方程.近年来对Birkhoff系统动力学的研究已取得一些重要进展,这些进展主要集中在该系统的积分理论[2]、动力学逆问题[3]、稳定性[4]、对称

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