Resonant orbit search and stability analysis for elongated asteroids

Periodic orbits are crucial in facilitating the understanding of the dynamical behavior of elongated asteroids.As a specific type of periodic orbit,resonant orbits can enrich the orbit design method of deep-space exploration missions.Herein,a dipole segment model for investigating the orbital dynamics of elongated asteroids is briefly introduced.A new numerical algorithm named the modified path searching method for identifying spin-orbit resonant orbits is proposed.Using the modified path searching and pseudo-arclength continuation methods,four spin-orbit resonant families for asteroid 2063 Bacchus are obtained.The distribution of eigenvalues and stability curves for the four resonant families are presented.In particular,some critical points corresponding to period-doubling and tangent bifurcations appear in the stability curves.

STOCHASTIC LAYER OF DUFFING'S EQUATION NEAR ITS SUBHARMONIC RESONANT ORBIT

In this Paper,the stochastic layer of Duffing's equation hosed on the chosen resonance is investigated.A general method is provided for studying the stochastic layer near the assigned resonant orbit. Several approximate critical conditions are given for the theoretical predictions of that stochastic layer. For non-dissipative Duffing's equation, two critical conditions are obtained when its global stochastic layer occurs and vanishes for the given resonance. In addition, a limit critical condition has been presented when all Possible resonances exist risible in the stochastic layer.Our results are compared with the critical conditions resulting from both Chirikov overlap method and renormalization techniques. Finally, using the cirtical conditions, numerical simulations are Performed to check our theoretical predictions of the stochastic layer based on the given resonance.

Averaging analyses for spacecraft orbital motions around asteroids

This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body＇s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stabil- ity regions in a numerical experiment. Some stability conclu- sions are obtained. As a typical example, it is shown in detail that near circular 1 ： 2 resonant orbit is always unstable.

Periodic Orbits in Rotating Second Degree and Order Gravity Fields

Periodic orbits in an arbitrary 2nd degree and order uniformly rotating gravity field are studied. We investigate the four equilibrium points in this gravity field. We see that close relation exists between the stability of these equilibria and the existence and stability of their nearby periodic orbits. We check the periodic orbits with non-zero periods. In our searching procedure for these periodic orbits, we remove the two unity eigenvalues from the state transition matrix to find a robust, non-singular linear map to solve for the periodic orbits. The algorithm converges well, especially for stable periodic orbits. Using the searching procedure, which is relatively automatic, we find five basic families of periodic orbits in the rotating second degree and order gravity field for planar motion, and discuss their existence and stability at different central body rotation rates.

Orbital Angular Momentum Generation Using Circular Ring Resonators in Radio Frequency

Electromagnetic field generators based on circular ring resonators, whose perimeters are integer times of equivalent wavelength, are well known to have attractive potential for producing radio vortexes carrying orbital angular momentum （OAM）. We study the radiation characteristics of the generators based on radiation vector and antenna array theory. The behaviors of radiation patterns, field intensity and phase distribution are investigated in detail, and show classical features of OAM beams. The evolution of the generators performance versus the OAM state is also analyzed. The proposed generators can be realized by all kinds of microwave transmission lines, verified by two different prototypes. The discussions and conclusions drawn in this study are useful and meaningful for the radio OAM generator design.

球后脂肪体积测定对甲状腺相关性眼病治疗时机的判定价值

目的探讨商业化软件计算球后脂肪体积,分析其与甲状腺相关性眼病(TAO)进展及预后的关系。方法收集2016年1月~2016年12月在我院内分泌科确诊的35例(70个眼眶)TAO患者的临床资料。测量1.5T眼眶MRI球后脂肪体积及眼外肌信号强度比值(SIR)分析其与临床各项指标的相关性,并收集12例(24个眼眶)健康人测量球后脂肪体积,初步比较TAO组及健康组体积的差异。结果脂肪体积与病程成正相关(r=0.480,P<0.01),病程6个月以内组与6~12个月组相比,脂肪体积差异不显著(P=0.084)。病程6个月以内组及病程6~12个月组球后脂肪体积均显著低于病程大于12个月组(P<0.01,P<0.05)。脂肪体积与突眼度存在相关性(r=0.622,P<0.01),突眼度每增加1 mm,球后脂肪体积将增加0.88 m L。临床活动性评分(CAS)与SIR值及促甲状腺素受体抗体(TRAb)存在相关性(r=0.536,r=0.416,P<0.01)。TAO组球后脂肪体积显著高于正常组(P<0.01)。结论 TAO病程1年以上可能是球后脂肪组织增多的高峰阶段,球后脂肪体积结合SIR值的测量有助于最佳激素治疗时机的探索及预后分析。

Optimal design of near-Earth asteroid sample-return trajectories in the Sun–Earth–Moon system

In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-kin-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.

Codimension-4 Resonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips

The paper studies a codimension-4 resonant homoclinic bifurcation with one orbit flip and two inclination flips, where the resonance takes place in the tangent direction of homoclinic orbit.Local active coordinate system is introduced to construct the Poincar′e returning map, and also the associated successor functions. We prove the existence of the saddle-node bifurcation, the perioddoubling bifurcation and the homoclinic-doubling bifurcation, and also locate the corresponding 1-periodic orbit, 1-homoclinic orbit, double periodic orbits and some 2n-homoclinic orbits.

Orbit design and mission planning for global observation of Jupiter

This paper presents the method created by the National University of Defense Technology(NUDT)team in the 10th China Trajectory Optimization Competition,which entails a 3-year observation mission of 180 regions on Jupiter.The proposed method can be divided into three steps.First,a preliminary analysis and evaluation via an analytical method is undertaken to decide whether the third subtask of the mission,i.e.,exploring the Galilean moons,should be ignored.Second,a near-optimal orbit for magnetic field observation is designed by solving an analytical equation.Third,a set of observation windows and their sequence are optimized using a customized genetic algorithm.The final index obtained is 354.505,ranking second out of all teams partaking in the competition.

Polarons in alkaline-earth-like atoms with multiple background Fermi surfaces

We study the impurity problem in a Fermi gas of 173Yb atoms near an orbital Feshbach resonance （OFR）, where a single moving particle in the 3p0 state interacts with two background Fermi seas of particles in different nuclear states of the ground 1S0 manifold. By employing wave function ansatz to molecule and polaron states, we investigate various properties of the molecule, the attractive polaron, and the repulsive polaron states. In comparison to the case where only one Fermi sea is populated, we find that the presence of an additional Fermi sea acts as an energy shift between the two channels of the OFR. In addition, quantum fluctuations near the Fermi level can also induce sizable effects to various properties of the attractive and repulsive polarons.

Hadron resonances as rovibrational states

A rovibrational model,including anharmonic,centrifugal,and Coriolis corrections,is used to calculate π,K,N,and ∑ orbital and radial resonances.The four orbital excitations of the n meson correspond to the/?(1235),ti2(1670),63(2030),and π4(2250)resonances.Its first four radial excitations correspond to the π(1300),π(1800),π(2070),and 7t(2360)resonances.The orbital excitations of the K meson are interpreted as the K_(1)(1270),K_(2)(1770),K_(3)(2320),and K_(4)(2500)resonances;its radial excitations correspond to the K(1460)and K(1830)resonances.The N orbital excitations are identified with the N(1520),N(1680),N(2190),N(2220),and N(2600)resonances.The first four radial excitations of the N family correspond to the N(1440),N(1880),N(2100),and N(2300)resonances.The orbital excitations of the ∑ baryon are associated with the ∑(1670),∑(1915),∑(2100),and ∑(2250)resonances,whereas its radial excitations are identified with the ∑(1660),∑(1770),and ∑(1880)resonances.The proposed rovibrational model calculations show a good agreement with the corresponding experimental values and allow for the prediction of hadron resonances,thereby proving to be useful for the interpretation of excited hadron spectra.