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研究Chetaev型约束力学系统Appell方程的Lie对称性和Lie对称性直接导致的守恒量.分析Lagrange函数和A函数的关系;讨论Chetaev型约束力学系统Appell方程的Lie对称性导致的守恒量的一般研究方法;在群的无限小变换下,给出Appell方程Lie对称性的定义和判据;得到Lie对称性的结构方程以及Lie对称性直接导致的守恒量的表达式.举例说明结果的应用.
关键词:
Appell方程
Chetaev 型约束力学系统
Lie对称性
守恒量 相似文献
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<正>The Mei symmetry and Mei conserved quantity of the Nielsen equation for a non-Chetaev-type non-holonomic non-conservative system are studied.The differential equations of motion of the Nielsen equation for the system,the definition and the criterion of Mei symmetry and the condition and the form of Mei conserved quantities deduced directly from the Mei symmetry for the system are obtained.Finally,an example is given to illustrate the application of the results. 相似文献
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A type of structural equation and conserved quantity which are directly induced by Mei symmetry of Nielsen equations for a holonomic system are studied.Under the infinitesimal transformation of the groups,from the definition and the criterion of Mei symmetry,a type of structural equation and conserved quantity for the system by proposition 2 are obtained,and the inferences in two special cases are given.Finally,an example is given to illustrate the application of the results. 相似文献
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Multi-symplectic variational integrators for nonlinear Schrdinger equations with variable coefficients 下载免费PDF全文
In this paper, we propose a variational integrator for nonlinear Schrdinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrdinger equations with variable coefficients, cubic nonlinear Schrdinger equations and Gross–Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space. 相似文献
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完整系统Appell方程Mei对称性的结构方程和Mei守恒量 总被引:4,自引:2,他引:2
研究完整系统Appell方程Mei对称性的结构方程和Mei守恒量.建立完整系统的Appell方程和系统的运动微分方程;在群的无限小变换下,给出完整系统Appell方程Mei对称性的定义和判据;得到用Appell函数表示的完整系统Appell方程Mei对称性的结构方程和Mei守恒量的表达式.举例说明结果的应用. 相似文献
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Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system 下载免费PDF全文
Mei symmetry and Mei conserved quantity of Appell
equations for a variable mass holonomic system are investigated.
Appell equations and differential equations of motion for a variable
mass holonomic system are established. A new expression of the total
first derivative of the function with respect of time t along the
systematic motional track curve, and the definition and the
criterion of Mei symmetry for Appell equations under the
infinitesimal transformations of groups are given. The expressions
of the structural equation and Mei conserved quantity for Mei
symmetry in Appell are obtained. An example is given to illustrate
the application of the results. 相似文献
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A field integration method for a weakly nonholonomic system is studied. The differential equations of motion of the system are established. The approximate solution of the holonomie system corresponding to the weakly nonholonomic system is obtained by using the field method. The restriction of nonholonomie constraint to initial conditions is added and the approximate solution of the weakly nonholonomic system is obtained. An example is given to demonstrate the application of the result. 相似文献
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研究准坐标下一般完整系统Nielsen方程的Mei对称性导致的Mei守恒量.给出一般完整系统Nielsen方程的Mei对称性的定义和判据,讨论一般完整系统Nielsen方程Mei对称性直接导致的Mei守恒量的条件及Mei守恒量的形式,并举例说明结果的应用. 相似文献