Four-Electron Quantum Ring in a Magnetic Field

We study a quantum ring （QR） with four electrons in a perpendicular external magnetic field B by exact diagonalization. The low-lying spectra of the QR as a function orb are obtained. A phase diagram is presented indicating that the angular momentum and the spin of the ground state of the QR may jump when B and/or the radius of the QR vary, and a corresponding analysis is performed. By plotting the density functions of the QR, the ground-state configuration is found to be a regular quadrangle. Furthermore, the features of the ground-state persistent current are revealed.     

Lie symmetries and invariants of constrained Hamiltonian systems

According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper.     

球坐标系中速度与加速度分量表示式的另一种推导

本文导出了单位矢量对时间导数的一般公式，并利用这一公式简便地推导出速度和加速度在球坐标系中的分量表达式.     

非惯性系机械能守恒定律

从非惯性系动力学方程出发，可导出对非惯性系的动能定理，在此基础上，引进惯性力势能Ｕｈ及对非惯性系的机械能 Ｅ’＝Ｕ’＋Ｕｈ＋Ｔ’，又可导出质点对非贯性系的机械能守恒律．此守恒律用来求解某些相对运动问题极为简便．     

广义Hojman定理

研究利用Lie对称的生成元τ(t,q,q·)和ξ_s(t,q,q·)来构造广义H ojman守恒 量，并讨论三种特殊情况，研究表明：Hojman守恒量是该广义守恒量的特例，且在Lie对称 的生成元的形式为τ(t,q)和ξ_s(t,q)时，该广义Hojman守恒量可以导出Lu tzky守恒 量，此外，还给出一个排除平凡守恒量的条件.最后，给出两个简单例子，作为所获得结果 的说明. 关键词： 动力学系统 广义Hojman定理 Lie对称 守恒量     

常数变易法在力学中的应用

利用常数变易法建立扰动运动方程，并举例说明了该方程的应用。     

Variational principle and dynamical equations of discrete nonconservative holonomic systems

By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler--Lagrange equations and Hamilton's canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative examples are also given.     

非完整非保守力学系统在相空间的Lie对称性与守恒量

在相空间引入无限小变换,研究非完整非保守力学系统运动微分方程的不变性和守恒量。建立Lie对称确定方程,得到Lie对称的结构方程和守恒量形式,并举例说明结果的应用。     

相对运动能量积分

在相对运动拉格朗日方程的基础上作勒让德变换得到动力学方程的正则形式，利用正则方程讨论了作相对运动的系统存在能量积分的条件。若约束是稳定的，主动力又是稳定的保守力，则系统的哈密顿函数就是总机械能，最后给出了相对运动机械能守恒定律。