非完整蛇形机器人系统的Lie对称性和守恒量

研究了蛇形机器人系统的Lie对称性和守恒量,给出该系统的Lie对称性积分方法.将蛇形机器人等效为一个由n节连杆构成的动力学系统,选择了恰当的广义坐标,给出蛇形机器人的动能、势能、Lagrange函数,以及所受的非完整约束,建立了蛇形机器人系统的第二类Lagrange方程;引入关于时间和广义坐标的无限小变换、相应的无限小...     

Non-Noether symmetries of Hamiltonian systems with conformable fractional derivatives

In this paper, we present the fractional Hamilton's canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. Firstly, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton's canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results.     

Efficient Excitation of a Symmetric Collective Atomic State with a Single-Photon Through Dipole Blockade

In the famous quantum communication scheme developed by Duan et al.[L.M.Duan,M.D.Lukin,J.I.Cirac,and P.Zoller,Nature(London) 414(2001) 413],the probability of successful generating a symmetric collective atomic state with a single-photon emitted have to be far smaller than 1 to obtain an acceptable entangled state.Based on strong dipole-dipole interaction between two Rydberg atoms,two simultaneous excitations in an atomic ensemble are greatly suppressed,which makes it possible to excite a mesoscopic cold atomic ensemble into a near-ideal singly-excited symmetric collective state accompanied by a signal-photon with near unity success probability.     

Fractional cyclic integrals and Routh equations of fractional Lagrange system with combined Caputo derivatives

In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagrange equations of the system are obtained under a combined Caputo derivative. Furthermore, the fractional cyclic integrals based on the Lagrange equations are studied and the associated Routh equations of the system are presented. Finally, two examples are given to show the applications of the results.     

Lagrange equations of nonholonomic systems with fractional derivatives

This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, based on these exchanging relationships, the Hamilton's principle is presented for non-conservative systems with fractional derivatives. Thirdly, Lagrange equations of the systems are obtained. Furthermore, the d'Alembert–Lagrange principle with fractional derivatives is presented,and the Lagrange equations of nonholonomic systems with fractional derivatives are studied. An example is designed to illustrate these results.     

A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems

In this paper Mei symmetry is introduced for a nonconservative system. The necessary and sufficient condition for a Mei symmetry to be also a Lie symmetry is derived. It is proved that the Mei symmetry leads to a non-Noether conservative quantity via a Lie symmetry, and deduces a Lutzky conservative quantity via a Lie point symmetry.     

Application of canonical coordinates for solving single-freedom constraint mechanical systems

This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conserva-tive and non-conservative constraint homonomic systems. The definition and properties of canonical coordinates are introduced. The relation between Lie point symmetries and the canonical coordinates of the constraint mechanical system are expressed. By this re-lation, the canonical coordinates can be obtained. Properties of the canonical coordinates and the Lie symmetry theory are used to seek the first integrals of constraint mechanical system. Three examples are used to show applications of the results.     

二次曲面区域泊松方程第一边值问题的格林函数解法

关于泊松方程第一边值问题,目前大部分研究仅给出了球域、圆域等情况的格林函数解法,而对其他类型的区域讨论甚少.该文从二次曲面成像公式出发,用电像法统一研究椭球面、双曲面、抛物面、球面等二次曲面区域内的泊松方程第一边值问题,旨在给出其各自的格林函数解及相应的第一积分表示式.研究发现,在近轴情况下,二次曲面区域内泊松方程第一边值问题的格林函数解及第一积分表示式有统一形式,该文最终给出了这种统一形式并分别对这几种二次曲面域进行了讨论.     

压电堆叠作动器的对称性求解

研究了压电堆叠作动器的对称性,并给出了系统存在的守恒量和对称性解.以轴向运动的压电堆叠作动器为研究对象,根据其结构特点,选取位移和磁链作为广义坐标,运用能量方法,建立了压电堆叠作动器的Lagrange(拉格朗日)方程.引入位移和磁链广义坐标的无限小群变换,分别研究了压电堆叠作动器的Noether对称性和Lie对称性,给出了广义Noether恒等式、广义Killing方程、广义Noether定理和Lie定理,计算了压电堆叠作动器存在的Noether对称性和Lie对称性的生成元,并给出了相应系统存在的守恒量.最后,利用得到的守恒量,给出了压电堆叠作动器对称性解,并计算了在控制电压变化的情况下位移和速度的动态响应曲线.