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periodic orbits in the Chermnykh problem

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Astrodynamics 2017年第1期1卷 41-55页

作者： Xiangyuan Zeng Kyle T.Alfriend School of Automation Beijing Institute of TechnologyBeijing 100081China Department of Aerospace Engineering Texas A&M UniversityCollege StationTexas 77840USA

periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as the engineering aspect for deep space explorations. The rotating mass dipole, referred to as the Chermnykh problem, is a good alternative model to study qualitative dynamical environments near elongated asteroids, like the asteroid 1620 Geographos, 216 Kleopatra, or 25143 Itokawa. In this paper a global searching method is adopted to search for periodic orbits around the dipole model based on the concept of Poincaré section of surface. Representative families of periodic orbits are illustrated with respect to all three topological cases of the dipole model. Topological transitions of orbits during iso-energetic continuations are also presented as well as identification of new types of periodic orbits.

关键词： periodic orbits the Chermnykh problem topological transition iso-energetic continuation

Study on periodic orbits around the dipole segment model for dumbbell-shaped asteroids

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Science China(Technological Sciences) 2018年第6期61卷 819-829页

作者： ZHANG YongLong ZENG XiangYuan LIU XiangDong School of Automation Beijing Institute of Technology Beijing 100081 China

Equilibrium points and periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as deep space exploring missions. The dipole segment is a good alternative model to study qualitative dynamical properties near dumbbell-shaped asteroids. In this paper, the dipole segment model and its equilibrium points are simply introduced. The stability of the two triangular equilibrium points of the system is numerically examined. Next, periodic orbits are presented around the dipole segment model in two different cases, in which triangular equilibria are linearly stable and unstable,respectively. New types of periodic orbits are illustrated in detail, including their orbital shapes, periods and the Jacobi *** orbital stability, topological classification and bifurcations of these orbits are also analyzed with numerical continuations.

关键词： dipole segment model equilibrium points periodic orbits topological classification

BIFURCATIONS OF periodic orbits IN THREE-WELL DUFFING SYSTEM WITH A PHASE SHIFT

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Journal of Systems Science & Complexity 2011年第3期24卷 519-531页

作者： Jicai HUANG Han ZHANG School of Mathematics and Statistics Central China Normal University Wuhan 430079 China College of Information Technical Science Nankai University Tianjin 300071 China.

Bifurcations of periodic orbits of three-well Duffing system with a phase shift are investigated in detail. The conditions of the existence and bifurcations for harmonics, subharmonics （2-order, 3- order and m-order） and superharmonics under small perturbations are given by using second-order averaging method and Melnikov＇s method. The influence of the phase shift on the dynamics is also obtained.

关键词： Bifurcations Melnikov's method periodic orbits second-order averaging three-well Duffing system.

One family of 13315 stable periodic orbits of non-hierarchical unequal-mass triple systems

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Science China(Physics,Mechanics & Astronomy) 2021年第1期64卷 108-113页

作者： XiaoMing Li XiaoChen Li ShiJun Liao MOE Key Laboratory of Disaster Forecast and Control in Engineering School of Mechanics and Construction EngineeringJinan UniversityGuangzhou510632China Department of Earth Atmospheric and Planetary SciencesMassachusetts Institute of TechnologyCambridge02139USA School of Civil Engineering and Transportation South China University of TechnologyGuangzhou510641China Department of Engineering Science University of OxfordOxfordOX13PJUK Center of Advanced Computing School of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong UniversityShanghai200240China School of Physics and Astronomy Shanghai Jiao Tong UniversityShanghai200240China

The three-body problem can be traced back to Newton in 1687,but it is still an open question *** that only a few periodic orbits of three-body systems were found in 300 years after Newton mentioned this famous *** triple systems are common in astronomy,practically all observed periodic triple systems are hierarchical(similar to the Sun,Earth and Moon).It has traditionally been believed that non-hierarchical triple systems would be unstable and thus should disintegrate into a stable binary system and a single star,and consequently stable periodic orbits of non-hierarchical triple systems have been expected to be rather ***,we report here one family of 135445 periodic orbits of non-hierarchical triple systems with unequal masses;13315 among them are *** with the narrow mass range(only 10-5)in which stable"Figure-eight"periodic orbits of three-body systems exist,our newly found stable periodic orbits have fairly large mass *** find that many of these numerically found stable non-hierarchical periodic orbits have mass ratios close to those of hierarchical triple systems that have been measured with astronomical *** implies that these stable periodic orbits of non-hierarchical triple systems with distinctly unequal masses quite possibly can be observed in *** investigation also suggests that there should exist an infinite number of stable periodic orbits of non-hierarchical triple systems with distinctly unequal *** that our approach has general meaning:in a similar way,every known family of periodic orbits of three-body systems with two or three equal masses can be used as a starting point to generate thousands of new periodic orbits of triple systems with distinctly unequal masses.

关键词： three-body problem non-hierarchical system periodic orbits

Numerical study on periodic orbits near 216 Kleopatra

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Journal of Beijing Institute of Technology 2016年第S2期25卷 99-103页

作者：张锋镝曾祥远刘向东 School of Automation Beijing Institute of Technology

Searching for periodic orbits around the polyhedral model of irregularly shaped asteroids suffers from inefficient calculations.A practical method is proposed to overcome the above problem by taking the asteroid 216 Kleopatra as an *** equations are briefly derived with respect to the two models,i.e.,the rotating dipole and the homogenous *** required initial variables of periodic orbits around the rotating mass dipole are first acquired,which are taken as initial guesses to obtain real orbits near Kleopatra in the polyhedral model.A planar single lobe orbit is presented to evaluate the effectiveness of the *** orbital properties and its stability are also discussed.

关键词： periodic orbits 216 Kleopatra the rotating mass dipole the polyhedral method

PERSISTENCE AND periodic orbits FOR TWO-SPECIES NON-AUTONOMOUS DIFFUSION LOTKA-VOLTERRA MODELS

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Applied Mathematics(A Journal of Chinese Universities) 2004年第4期19卷 359-366页

作者： ChenFengde Dept.ofMath. FuzhouUniv.Fujian350002China

A non-autonomous competing system is investigated in this paper,where the species x can diffuse between two patches of a heterogeneous environment with barriers between patches,but for species y,the diffusion does not involve a barrier between patches,further it is assumed that all the parameters are time *** is shown that the system can be made persistent under some appropriate ***,sufficient conditions that guarantee the existence of a unique positive periodic orbit which is globally asymptotic stable are derived.

关键词： persistence diffusion periodic orbits global stability.

Stable periodic orbits for spacecraft around minor celestial bodies

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Astrodynamics 2018年第1期2卷 69-86页

作者： Yu Jiang Jurgen Arno Schmidt Hengnian Li Xiaodong Liu Yue Yang State Key Laboratory of Astronautic Dynamics Xi'an Satellite Control CenterXi'an 710043China School of Aerospace Engineering Tsinghua UniversityBeijing 100084China Astronomy Research Unit University of OuluFinland School of Software Engineering Xi'an Jiaotong UniversityXi'an 710049China

We are interested in stable periodic orbits for spacecraft in the gravitational eld of minor celestial *** stable periodic orbits around minor celestial bodies are useful not only for the mission design of the deep space exploration,but also for studying the long-time stability of small satellites in the large-size-ratio binary *** irregular shapes and gravitational elds of the minor celestial bodies are modeled by the polyhedral *** the topological classi cations of periodic orbits and the grid search method,the stable periodic orbits can be calculated and the topological cases can be ***,we nd ve di erent types of stable periodic orbits around minor celestial bodies:(1)stable periodic orbits generated from the stable equilibrium points outside the minor celestial body;(2)stable periodic orbits continued from the unstable periodic orbits around the unstable equilibrium points;(3)retrograde and nearly circular periodic orbits with zero-inclination around minor celestial bodies;(4)resonance periodic orbits;(5)near-surface inclined periodic *** take asteroids 243 Ida,433 Eros,6489 Golevka,101955 Bennu,and the comet 1P/Halley for examples.

关键词： asteroid comet deep space exploration periodic orbits stability orbit design

periodic orbits in the Photogravitational Restricted Problem When the Primaries Are Triaxial Rigid Bodies

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International Journal of Astronomy and Astrophysics 2016年第1期6卷 111-121页

作者： Preeti Jain Rajiv Aggarwal Amit Mittal Abdullah Department of Mathematics A.R.S.D. College University of Delhi New Delhi India Department of Mathematics Sri Aurobindo College University of Delhi New Delhi India Department of Mathematics College of Science in Zulfi Majmaah University Riyadh KSA

We have studied periodic orbits generated by Lagrangian solutions of the restricted three-body problem when both the primaries are triaxial rigid bodies and source of radiation pressure. We have determined periodic orbits for different values of (h is energy constant;μ is mass ratio of the two primaries;are parameters of triaxial rigid bodies and are radiation parameters). These orbits have been determined by giving displacements along the tangent and normal at the mobile co-ordinates as defined in our papers (Mittal et al. [1]-[3]). These orbits have been drawn by using the predictor-corrector method. We have also studied the effect of triaxial bodies and source of radiation pressure on the periodic orbits by taking fixed value of μ.

关键词： Restricted Three-Body Problem periodic orbits Triaxial Rigid Body Radiation Pressure

periodic orbits on AF-Symplectic Manifolds

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Tsinghua Science and Technology 1997年第3期2卷 99-102,108页

作者：马仁义 Department of Applied Mathematics Tsinghua University Beijing 100084

The method by McDuff is used to get the existence of the J holomorphic sphere in some symplectic Manifolds and then the J holomorphic sphere is perturbed to split a periodic solution of Hamiltonian systems in these sy... 详细信息

关键词： symplectic geometry dynamical systems periodic orbits