共查询到17条相似文献,搜索用时 156 毫秒
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提出构造二阶微分方程的Lagrange函数和Hamilton函数的新路径. 将二阶方程写成一阶方程组并构造出对应的一阶Lagrange函数后,直接从一阶Lagrange函数导出二阶Lagrange函数和Hamilton函数. 利用上述方法得到若干耗散和类耗散系统的一阶和二阶Lagrange函数以及Hamilton函数;讨论了这种方法的优点. 举例说明所得结果的应用.
关键词:
逆问题
耗散系统
Lagrange函数
Hamilton函数 相似文献
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研究Lagrange系统的Mei对称性直接导致的一种守恒量. 给出系统的Mei对称性的定义和判据方程, 得到系统Mei对称性直接导致的一种守恒量的条件和形式,并举例说明结果的应用.
关键词:
Lagrange系统
Mei对称性
守恒量 相似文献
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A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results. 相似文献
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A gradient system and a skew-gradient system can be merged into a combined gradient system. The differential equations of the combined gradient system are established and its property is studied. If a mechanical system can be represented as a combined gradient system, the stability of the mechanical system can be studied by using the property of the combined gradient system. Some examples are given to illustrate the applications of the results. 相似文献
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This paper focus on the problem of global Lagrange stability for neutral-type inertial neural networks with discrete and distributed time delays. By choosing a proper variable substitution, an inertial neural network consisting of second-order differential equations can be converted into a first-order differential model. The sufficient conditions of the inertial neural network with neutral delay are derived by constructing suitable Lyapunov-Krasovskii functional candidates, introducing new free weighting matrices, utilizing inequality techniques and analytical method. Through the LMI condition, we analyze the global exponential stability of the delayed inertial neural networks in Lagrange sense. Meanwhile, the global exponential attractive set is also given. Finally, some example is given to illustrate our theoretical results. 相似文献
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LIU Chang ZHU Na MEI Feng-Xiang GUO Yong-Xin 《理论物理通讯》2008,50(11):1065-1068
In this paper the conformal invariance by infinitesimal transformations of first-order Lagrange systems is discussed in detail. The necessary and sumeient conditions of conformal invariance by the action of infinitesimal transformations being Lie symmetry simultaneously are given. Then we get the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results. 相似文献