事件空间中完整力学系统的梯度表示

本文研究事件空间中完整力学系统的梯度表示和分数维梯度表示, 建立系统的微分方程并将其表示为一阶形式, 给出系统成为梯度系统的条件以及成为分数维梯度系统的条件. 最后, 举例说明结果的应用.     

一阶Lagrange系统的梯度表示

研究一阶Lagrange系统的梯度表示. 给出一阶Lagrange系统可成为梯度系统的条件. 利用梯度系统的性质研究系统的稳定性. 给出例子说明结果的应用. 关键词： 一阶Lagrange系统 梯度系统 稳定性     

混料分类模型的最优设计

由于混料试验中的响应变量常受到定性因子的影响,故通常采用分类模型来建模.通过已有的D-最优设计的结论导出A-,R-最优设计的方差函数以及等价条件,并给出实例分析.     

Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms

In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation,applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities.     

A new conserved quantity of mechanical systems with differential constraints

A new conserved quantity of non-Noether symmetry for the mechanical systems with differential constraints is studied. First, the differential equations of motion of the systems are established. Then, the determining equations and restriction equations of the non-Noether symmetry are obtained and a new conserved quantity is given. Finally, an example is given to illustrate the application of the results.     

Lagrange系统在施加陀螺力后的对称性

研究Lagrange系统在施加陀螺力后的Noether对称性与Lie对称性.给出系统在施加陀螺力后 ，可保持其Noether对称性与Noether守恒量的条件.给出系统在施加陀螺力后，可保持其Lie 对称性与Hojman守恒量的条件.最后，举例说明结果的应用. 关键词： Lagrange系统 陀螺力 对称性 守恒量     

求解微分方程的Hojman方法

首先，将Hojman用于求解二阶微分方程组守恒量的方法推广并应用于一阶微分方程组，特别是奇数维微分方程组的积分问题.然后，证明 Hojman定理是本文定理的特殊情形.最后，举例说明结果的应用. 关键词： 微分方程 Hojman定理 守恒量 积分     

混料分类模型的最优设计北大核心CSCD

由于混料试验中的响应变量常受到定性因子的影响,故通常采用分类模型来建模.通过已有的D-最优设计的结论导出A-,R-最优设计的方差函数以及等价条件,并给出实例分析.     

Type of integral and reduction for a generalized Birkhoffian system

This paper studies a type of integral and reduction of the generalized Birkhoffian system. An existent condition and the form of the integral are obtained. By using the integral, the dimension of the system can be reduced two degrees. An example is given to illustrate the application of the results.     

Lagrange--Noether method for solving second-order differential equations

The purpose of this paper is to provide a new method called the Lagrange--Noether method for solving second-order differential equations. The method is, firstly, to write the second-order differential equations completely or partially in the form of Lagrange equations, and secondly, to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.