Singular Points, Closed Orbits, Stable Manifolds and Unstable Manifolds of Second Order Autonomous Birkhoff Systems

Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.

The closed-orbit and the photoabsorption spectra of the Rydberg hydrogen atom between two parallel metallic surfaces

Using the closed orbit theory, we study the classical motion and calculatethe photoabsorption spectra of Rydberg hydrogen atom between two parallel metallic surfaces. The results show that the metallic surfaces have a significant effect on the photoabsorption process. When the distances between the hydrogen atom and the two metallic surfaces are close to a critical value dc, the number of the closed orbits is the greatest. When the distance larger or smaller than dc, the number of the closed orbits decreases and the absorption spectra are shown to exhibit a damping oscillation. This work is an interesting new application of closed-orbit theory and is of potential experimental interest.

Study of Electron Orbits for Formation of Toroidal Closed Flux Surface by ECH

Electron orbits under the external vertical field （Bv） and the self poloidal field of the toroidal plasma current in a toroidal geometry are investigated by using analytic model fields in order to search for the conditions of occurence of appropriate confinement asymmetry of fast electrons along the field lines. This asymmetry efficiently and quickly generates a toroidal current, which may close the field lines in ECH-started plasmas. It is analytically shown that the characteristics of confinement asymmetry depend on the product of the major radius and the strength of the external vertical field. The results suggest that in large devices By should be lowered and also some artificial means to speed up the pitch angle scattering for the fast electrons at a higher energy range are beneficial to generate the toroidal current in order to close the filed

6-3 Closed Orbit Correction in Electron Cooler Section at CSRe

The injecting section and the cooler section are apart from each other at CSRm, while the electron cooler systemis installed at the injecting section of CSRe[1]. So for the CSRe we not only need to satisfy the beam injectingcondition but also need to satisfy the beam cooling condition. At present, we use the ramping bump and the kickerto inject beam, and after injection the bump disappear quickly and the beam goes to the cooling orbit and begincooling. This method has a disadvantage that the beam cooling condition cannot be satised until the bump isdown. In the past year, we try to nd a new method to correct the orbit of cooler section. Instead of using rampingbump we use the xed bump to satisfy the injecting and the cooling condition at the same time.

含参非线性扰动系统的闭轨分叉分析

研究了一类含参非线性系统的闭轨分叉问题,找到并确定了系统在平衡点附近的极限环及其稳定性.基于后继函数法,引入曲线坐标变换找到系统的后继函数,进而判断该闭轨为二重极限环.得到该系统极限环随参数变化从无到有,再到分裂为多个极限环的闭轨分叉现象.通过数值模拟,验证了系统随参数变化出现极限环的动力学特性.

FIXED POINT WITH ORBITAL DIAMETRAL FUNCTION

A foremost general contraction condition is introduced to prove the existence of fixed points for a self-mapping in a somplete metric space whose orbital diametral functions are closed. This condition covers not only the Kannan type but also covers Reich, and Hardy and Roger's type contractive conditions. An example is given in its support.

An Orbital Period Study of the Contact Binary CK Bootis

Various times of light minima of the contact binary CK Boo are compiled and the correspnoding O C curve is analyzed with Kalimeris at al.’s method (1994). It is shown that the orbital period varies in a quasi sinusoidal form with a period of about 14 years and an amplitude of 0.26 × 10 -5 days while it undergoes a secular period increase dP/dE =+4 97 × 10 -7 days/year. The mechanisms that could explain the changes in the orbital period are also discussed.

一阶常微分方程可积性研究的初等方法

本文针对一类一阶常微分方程,给出基于变量代换和极坐标变换的求解一阶常微分方程通积分的初等方法,两种方法所得的结果完全一致,从而该方程的可积性可知.进一步地,基于通积分的显式表达式,我们分析获得该方程的全局轨道分布,得到经过退化平衡点的一族周期闭轨的存在性.

火星环绕器火卫一抵近探测拓展任务设想轨道设计与分析

针对“天问一号”火星环绕器火卫一抵近探测拓展任务设想开展了任务轨道设计与分析,将主任务结束后的状态作为拓展任务的输入,对拓展任务轨道、变轨策略及燃料代价进行设计。通过分析得出,可利用火星摄动力调整近火点幅角使得环绕器轨道与火卫一轨道相交,且相交频率与半长轴和偏心率相关。为提高相交次数需进行降轨,进一步分析了利用火星大气辅助降轨以降低燃料消耗、提高轨道相交次数的可能性,最后通过调相机动的方式使环绕器完成火卫一抵近探测任务。仿真结果表明:所设计的拓展任务轨道及变轨策略的速度增量代价合理可行,可为后续火星环绕探测任务轨道设计提供参考。

Studies of closed orbit correction and slow orbit feedback for the SSRF storage ring

Details of the active ways to suppress Closed Orbit Distortion （COD）, including bending magnet sorting and survey and alignment of the magnets, are discussed based on the studies of affections to the COD by the bending magnet field error and the misalignment of quadrupoles. The closed orbit correction and the Slow Orbit Feed Back （SOFB） system for the SSRF storage ring are presented in this paper. With these available methods, better results were obtained during the commissioning period with 3 GeV beam energy.

Numerical Method for Following the Closed Orbits in High-dimensional Space

The spline interpolation is used to approximate the closed orbits, and the problem of following the dosed orbit in large-scale is turned to tracking the solution curve of a nonlinear equation system in higher-dimensional space. The deformation of the closed orbit of Lorenz equation is calculated.

Study of closed orbit response to magnet vibrations at the SSRF storage ring

This paper presents the analytical and simulation responses of the closed orbit distortion in the SSRF storage ring to random and plane wave like magnet vibrations respectively. It is shown that the use of girder is very beneficial in the view of suppressing this response function. Effect of the independently supported gradient bending magnets to the closed orbit response is given. An analytic formula is written to give a rough estimate of the closed orbit distortion due to ground motion, taking into account the closed orbit response function and girder transfer function. As an example, the result of SSRF case is given.

The Closed Orbits of a Class of Cubic Vector Fields in R^(3)

In this paper,we investigate the isolated closed orbits of two types of cubic vector fields in R^3 by using the idea of central projection transformation,which sets up a bridge connecting the vector field X(x)in R^3 with the planar vector fields.We have proved that the cubic vector field in R^3 can have two isolated closed orbits or one closed orbit on the invariant cone.As an application of this result,we have shown that a class of 3-dimensional cubic system has at least 10 isolated closed orbits located on 5 invariant cones,and another type of 3-dimensional cubic system has at least 26 isolated closed orbits located on 13 invariant cones or 26 invariant cones.

On the detection of closed orbits in time-dependent systems by using double-pulse lasers

In the photodetachment of atoms or negative ions by a double-pulse laser, the first pulse of the double-pulse laser generates waves and the delayed second pulse may detect them. The phenomenon of the excitation and detection of waves by a double-pulse laser can be used to identify the closed orbits in the system. We demonstrate this phenomenon with a negative hydrogen ion(H^-) by analyzing the total population excited by a double-pulse laser in a timedependent field for different physical parameters. By analyzing the total excited population using a double-pulse laser, we can uncover all the closed orbits existing in the system. We demonstrate that this can be realized by scanning the first pulse position and the time delay between the two pulses.

基于量子轨道角动量的激光近程目标探测方法

激光近程探测受到云、烟、雾等自然因素的严重干扰,容易产生虚警等问题。针对该问题,结合涡旋激光大气散射理论设计了一种量子轨道角动量激光目标近程探测系统,并实施了不同能见度烟雾环境下的近程目标探测试验,对比了涡旋光束与高斯光束的目标回波信号强度。初步验证试验结果表明:涡旋光束相较于高斯光束有更优的烟雾穿透能力。

Conditions of C0 flows on closed surfaces having the pseudo-orbit tracing property

Let M be a closed surface,orientable or non-orientable,and let f be a C0 flow on M of which all singular points are isolated.Then f has the pseudo-orbit tracing property if and only if (i) for any x∈M,both the ω-limit set ω(x) and the α-limit set α(x) of x contain only one orbit; (ii) for any regular point x of f,if ω(x) is not quasi-attracting,then α(x) is quasi-exclusive; (iii) every saddle point of f is strict,and at most 4-forked.

Evaluation of Orbital- and Ground State Energies of Some Open- and Closed-Shell Atoms over Integer and Noninteger Slater Type Orbitals

Ab initio calculations of the orbital and the ground state energies of some open- and closed-shell atoms over Slater type orbitals with quantum numbers integer and Slater type orbitals with quantum numbers noninteger have been performed. In order to increase the efficiency of these calculations the atomic two-electron integrals were expressed in terms of incomplete beta function. Results were observed to be in good agreement with the literature.

ON CLOSED ORBIT FOR A CLASS OF PLANAR SYSTEMS OF HIGH DEGREE

or a class of planar polynomial differential systems of degree p+q, arising from biochemical reactions, there are given conditions of parameters under which the systems produce Hopf bifurcation with limit cycles appearing, or have no closed orbits.

单个航天器对Walker星座中多卫星的近距离接近

通过设计航天器轨道,可使航天器发射入轨后无需机动即实现对Walker星座中非共轨的多颗卫星的快速、近距离接近。给出了该轨道的搜索方法以及基于星座特性的代换法,并给出了仿真示例。

基于轨道根数的低轨卫星轨道预测算法

光电设备因太阳夹角变化、轨道遮挡等原因无法对卫星进行自动跟踪时,需要对卫星轨道进行预测。本文针对利用卫星轨道根数进行轨道预报时难以同时满足实时性和精度要求的问题,提出了一种新的基于轨道根数的卫星轨道预测方法。分析了卫星轨道的运行规律,根据低轨卫星的运行特点,利用椭圆曲线对卫星轨道进行预测,并对卫星轨道的轨道方程进行了近似处理。通过引入一些冗余变量简化了卫星轨道解算模型,在保证计算实时性的前提下,大大提高了轨道预测精度。实验显示:采用线性外推方法对卫星轨道进行预测时,预测5s后,轨道预测的偏差会增大到10″,而采用本文提出的基于轨道根数的卫星轨道预测算法,预测50s后的最大预测偏差均不超过2″,极大地提高了卫星轨道预测精度,实现了光电设备在无法对卫星进行自动跟踪时,能够对卫星进行"盲跟踪"。