Non-Noether symmetries and conserved quantities of the Lagrange mechano-electrical systems

This paper focuses on studying non-Noether symmetries and conserved quantities of Lagrange mechano-electrical dynamical systems. Based on the relationships between the motion and Lagrangian, we present conservation laws on non-Noether symmetries for Lagrange mechano-electrical dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry of the systems. The work also gives connections between the non-Noether symmetries and Lie point symmetries, and further obtains Lie invariants to form a complete set of non-Noether conserved quantity. Finally, an example is discussed to illustrate these results.     

Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices

The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results.     

The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems

This paper investigates the Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems. The variational principle of discrete mechanics, from which discrete motion equations of systems are deduced, is generalized to the case of including the time variational. The requirement for an invariant group transformation is defined to be the Lie symmetry and the criterion when the Noether conserved quantities may be obtained from Lie symmetries is also presented. An example is discussed for applications of the results.     

离散Lagrange系统的Lie对称性

研究离散Lagrange系统的Lie对称性. 根据离散变分原理建立离散系统的运动方程. 给出离散运动方程Lie对称性的定义和确定方程. 举例说明结果的应用. 关键词： 离散Lagrange系统 离散变分原理 Lie对称性 确定方程     

控制混沌的原理及应用

概述了控制混沌使其转化为周期性动力学行为的几种主要方案，包括对受控系统施加外激励型控制的输送控制，对受控混沌系统的可控参数施加小摄动以稳化周期性轨道的ＯＧＹ方法，以及应用自控技术中的自适应控制和常规反馈控制。也介绍了控制混沌在数值实验和实验室实验中的应用。最后还简介了控制混沌的若干发展动向。     

非轴对称陀螺体自激运动的定性分析

研究非轴对称陀螺体在自激控制力矩作用下的姿态运动.将无力矩状态的两个初积分的积分常数T和G2作为描述自激运动的状态变量建立其微分方程.利用受扰运动在(T,G2)空间中的相轨迹判断稳态运动的稳定性,并进行了数值验证.     

航天器姿态动力学中的稳定性、分岔和混沌

讨论航天器姿态动力学中的若干非线性问题．总结了多刚体、柔性体和充液体航天器姿态 稳定性的研究成果．综述了航天器姿态运动的分岔和混沌的研究进展．展望了该领域的发展趋势．     

工程专业非线性动力学教材建设——介绍《非线性动力学》一书

非线性动力学不仅是基础研究中的重要课题,也有广阔的应用前景．随着理论研究的深入,其工程应用愈来愈受到重视．非线性动力学不仅是数学、物理学科教学内容,而且正在成为工程专业学生特别是研究生教学内容的一个重要方面．工程问题的研究者有必要理解和掌握非线性动力学的概念和方法,以便能从新的角度考察各自专业中的研究课题． 国外从１９８４年起陆续出版以混饨为主要内容的非线性动力学教材文献出,为最早的面向工程专业的非线性动力学教材,但除个别例子外与数理专业教材差别不大．文献［２～５］都是有工程专业特色的教材,但理…     

车路耦合非线性振动高阶Galerkin截断研究

将移动车辆模型化为运动的两自由度质量-弹簧-阻尼系统,道路模型化为立方非线性黏弹性地基上的弹性梁,并将路面不平度设定为简谐函数．通过受力分析,建立车路非线性耦合振动高阶偏微分方程．采用高阶Galerkin截断结合数值方法求解耦合系统的动态响应．首次研究不同截断阶数对车路耦合非线性振动动态响应的影响,确定Galerkin截断研究车路耦合振动的收敛性．研究结果表明,对于软土地基的沥青路面,耦合振动的动态响应,需要150阶以上的截断才能达到收敛效果．并通过高阶收敛的Galerkin截断研究了系统参数对车路耦合非线性振动动态响应的影响.     

一类高阶非线性波方程的子方程与精确行波解

结合子方程和动力系统分析的方法研究了一类五阶非线性波方程的精确行波解.得到了这类方程所蕴含的子方程, 并利用子方程在不同参数条件下的精确解, 给出了研究这类高阶非线性波方程行波解的方法, 并以Sawada Kotera方程为例, 给出了该方程的两组精确谷状孤波解和两组光滑周期波解.该研究方法适用于形如对应行波系统可以约化为只含有偶数阶导数、一阶导数平方和未知函数的多项式形式的高阶非线性波方程行波解的研究.