变质量非完整系统Tzénoff方程的Lie对称性与其导出的守恒量

航天器运行系统大都属于变质量力学系统,变质量力学系统的对称性和守恒量隐含着航天系统更深刻的物理规律.本文首先导出了变质量非完整力学系统的Tzénoff方程,然后研究了变质量非完整力学系统Tzénoff方程的Lie对称性及其所导出的守恒量,给出了这种守恒量的函数表达式和导出这种守恒量的判据方程.该研究结果对进一步探究变质量系统所遵循的守恒规律具有一定的理论价值.     

碳团簇奇偶性研究

用Ｈｃｋｅｌ－Ｈｕｂｂａｒｄ理论，考虑多电子体系的组态相互作用，计算出线性碳原子和离子团簇（Ｃｎ，）的π电子体系能量Ｅｎ。两相邻团簇的能量差△Ｅｎ＝｜Ｅｎ－Ｅｎ－１｜与ｎ的关系显示出与实验相符合的奇偶性质，从而揭示出碳团簇的奇偶性与该类团簇的π电子体系有关。     

完整系统Tzénoff方程的Mei对称性直接导致的另一种守恒量

研究了完整力学系统Tzénoff方程Mei对称性直接导致的另一种守恒量,给出了这种守恒量的函数表达式和导致这种守恒量的确定方程.利用该方法比以往更易找到守恒量.最后举例说明了新结果的应用.     

只有一个S价电子元素团簇的奇偶性研究

将Ｈｕｃｋｅｌ－Ｈｕｂｂａｒｄ方法推广应用于研究只有一个ｓ价电子元素（用字母Ａ标记这类元素）的团簇。计算了结构为团簇的最稳定结构。最后计算了该类团簇线性结构的ｓ价电子体系能量Ｅ＿ｎ，两相邻团簇的ｓ价电子体系的能量差ΔＥ＝｜Ｅ＿ｎ－Ｅ＿（ｎ－１）｜与原子数ｎ的关系显示出与实验相符合的奇偶性质。     

Conformal invariance and conserved quantities of dynamical system of relative motion

This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.     

Lagrange-Maxwell系统的Lie对称性与守恒量

由微分方程在无限小主为换下的不变性,定义Ｌａｇｒａｎｇｅ－Ｍａｘｗｅｌｌ方程元限元小变失生成元,给出Ｌｉｅ对称性的确定方程,得到结构方程和守恒量。     

转动相对论系统的Lie对称性和守恒量

研究转动相对论性完整与非完整力学系统的Lie对称性和守恒量.定义转动相对论力学系统的无限小变换生成元,利用微分方程在无限小变换下的不变性,建立转动相对论性力学系统的Lie对称确定方程,得到结构方程和守恒量的形式,并给出应用实例.     

An application of a combined gradient system to stabilize a mechanical system

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.     

光的衍射法测量杨氏模量

拉伸法测量金属丝杨氏模量的关键是如何测准金属丝在拉力作用下的微小伸长量。本文利用光的衍射法可以较精确地测量长度变化这一特点，对钢丝的杨氏模量进行了测量，给出测量杨氏模量的一种新方法。     

Algebraic structure and Poisson integrals of a rotational relativistic Birkhoff system

We have studied the algebraic structure of the dynamical equations of a rotational relativistic Birkhoff system. It is proven that autonomous and semi-autonomous rotational relativistic Birkhoff equations possess consistent algebraic structure and Lie algebraic structure. In general, non-autonomous rotational relativistic Birkhoff equations possess no algebraic structure, but a type of special non-autonomous rotational relativistic Birkhoff equation possesses consistent algebraic structure and consistent Lie algebraic structure. Then, we obtain the Poisson integrals of the dynamical equations of the rotational relativistic Birkhoff system. Finally, we give an example to illustrate the application of the results.