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Close relative motion on distant retrograde orbits

Chinese Journal of Aeronautics 2023年第3期36卷 335-356页

作者： Chihang YANG Ming WANG Hao ZHANG University of Chinese Academy of Sciences Beijing 100049China Key Laboratory of Space Utilization Technology and Engineering Center for Space UtilizationChinese Academy of SciencesBeijing 100094China

Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital ***,the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO ***,as the reference DROs are obtained through numerical methods,the close relative motions on DROs are non-analytical,which severely limits the design of relative *** this paper,a novel approach is proposed to construct the analytical solution of bounded close relative motion on *** linear dynamics of relative motion on DRO is established at *** preliminary forms of the general solutions are obtained based on the Floquet *** the general solutions are classified as different modes depending on their periodic components.A new parameterization is applied to each mode,which allows us to explore the geometries of quasi-periodic modes in *** each mode,the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier *** this way,the analytical bounded relative motion on DRO is *** on the analytical expression,the characteristics of different modes are comprehensively *** natural periodic mode is always located on the single side of the target spacecraft on DRO and is appropriate to be the parking orbits of the rendezvous and *** the basis of quasi-periodic modes,quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per *** fly-around formation can support observations to targets on DRO from multiple viewing *** the fly-around formation is validated in a more practical ephemeris model.

关键词： Distant retrograde orbits Ephemeris model Floquet theory Formation flight relative motion Spacecraft Three-body problem Transfer singularity

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Integrated modeling of spacecraft relative motion dynamics using dual quaternion

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Journal of Systems Engineering and Electronics 2018年第2期29卷 367-377页

作者： PENG Xuan SHI Xiaoping GONG Yupeng Control and Simulation Center Harbin Institute of Technology Research Center of Satellite Technology Harbin Institute of Technology

To realize high accurate control of relative position and attitude between two spacecrafts, the coupling between position and attitude must be fully considered and a more precise model should be established. This paper breaks the traditional divide and conquer idea, and uses a mathematical tool, namely dual quaternion to establish the integrated 6 degree-of-freedom(6-DOF) model of relative position and attitude, which describes the coupled relative motion in a compact and efficient form and needs less information of the target. Considering the complex operation rules and the unclarity of the current relative motion model in dual quaternion, necessary mathematical foundations are given at first, followed by clear and detailed modeling process and analysis. Finally a generalized proportion-derivative(PD) controller law is designed. The simulation results show that based on the integrated model established by dual quaternion, this control law can achieve a high control accuracy of relative motion.

关键词： relative motion dual quaternion position and attitude coupling integrated modeling

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Lie symmetry and Hojman conserved quantity of a Nielsen equation in a dynamical system of relative motion with Chetaev-type nonholonomic constraint

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Chinese Physics B 2011年第12期20卷 259-263页

作者：王肖肖孙现亭张美玲解银丽贾利群 School of Science Jiangnan University School of Electric and Information Engineering Pingdingshan University

The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.

关键词： nonholonomic constraint of Chetaev's type relative motion Nielsen equation Hojman conserved quantity

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Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion

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Chinese Physics B 2012年第10期21卷 17-21页

作者：张美玲王肖肖韩月林贾利群 School of Science Jiangnan University

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are *** definition and criterion of the Mei symmetry of Appell equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups are *** structural equation of Mei symmetry of Appell equations and the expression of Mei conserved quantity deduced directly from Mei symmetry for a variable mass holonomic system of relative motion are ***,an example is given to illustrate the application of the results.

关键词： variable mass relative motion Appell equations Mei conserved quantity

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Lie-Form Invariance of the Nonholonomic System of relative motion in Event Space

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Communications in Theoretical Physics 2007年第5X期48卷 795-798页

作者： HOU Qi-Bao LI Yuan-Cheng WANG Jing XIA Li-Li College of Physics Science and Technology China University of Petroleum Dongying 257061 China

In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative motion in event space is given. Secondly, the Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. An example is given to illustrate the application of the results.

关键词： event space nonholonomic system relative motion Lie-form invariance conserved quantity

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Integrating Factors and Conservation Theorems of Nonholonomic Dynamical System of relative motion

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Communications in Theoretical Physics 2007年第2期47卷 217-220页

作者： QIAO Yong-Fen ZHAO Shu-Hong LI Ren-Jie Engineering College of Northeast Agricultural University Harbin 150030 China Faculty of Science Laiyang Agricultural College Laiyang. 265200 China

The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.

关键词： nonholonomic system relative motion integrating factor conservation theorem

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Linearized relative motion equations through orbital element differences for general Keplerian orbits

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Astrodynamics 2018年第3期2卷 201-215页

作者： Zhaohui Dang Hao Zhang Northwestern Polytechnical University Xi’an 710072China Technology and Engineering Center for Space Utilization Beijing 100194China

A new formulation of the orbital element-based relative motion equations is developed for general Keplerian *** new solution is derived by performing a Taylor expansion on the Cartesian coordinates in the rotating frame with respect to the orbital *** resulted solution is expressed in terms of two different sets of orbital *** first one is the classical orbital elements and the second one is the nonsingular orbital *** of them,however,the semi-latus rectum and true anomaly are used due to their generality,rather than the semi-major axis and mean anomaly that are used in most *** specific selection for orbital elements yields a new solution that is universally applicable to elliptic,parabolic and hyperbolic *** is shown that the new orbital element-based relative motion equations are equivalent to the Tschauner–Hempel equations.A linear map between the initial orbital element differences and the integration constants associated with the solution of the Tschauner–Hempel equations is ***,the presented solution is validated through comparison with a high-fidelity numerical orbit *** numerical results demonstrate that the new solution is computationally effective;and the result is able to match the accuracy that is required for linear propagation of spacecraft relative motion over a broad range of Keplerian orbits.

关键词： relative motion Keplerian orbits orbital element linearized equations

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The forms of three-order Lagrangian equation in relative motion

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Chinese Physics B 2005年第2期14卷 244-246页

作者：马善钧刘明萍黄沛天 CollegeofPhysicsandCommunicationElectronics JiangxiNormalUniversityNanchang330027China

In this paper, the general expressions of three-order Lagrangian equations in a motional coordinate system are obtained. In coordinate systems with some specific forms of motion, the expressions corresponding to these... 详细信息

关键词： three order Lagrangian equations relative motion time rate of change of force

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Algebraic Structure of the Dynamical Equations of Holonomic Mechanical System in relative motion

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Journal of Beijing Institute of Technology 1998年第1期7卷 12-18页

作者：张毅梅凤翔北京理工大学应用力学系

Aim To study an algebraic of the dynamical equations of holonomic mechanical systems in relative motion. Methods The equations of motion were presented in a contravariant algebraic form and an algebraic product was determined. Results and Conclusion The equations a Lie algebraic structure if any nonpotential generalized force doesn't exist while while the equations possess a Lie-admissible algebraic structure if nonpotential generalized forces exist .

关键词： analytical mechanics holonomic system relative motion Lie-admissible algebra

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How are multiple satellites seen from the ground? relative apparent motion and formation stabilization

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Astrodynamics 2024年第1期8卷 121-134页

作者： Kenta Nakajima Yasuhiro Yoshimura Hongru Chen Toshiya Hanada Department of Aeronautics and Astronautics Kyushu University744 Motooka Nishi-kuFukuoka819-0395Japan

This paper answers how multiple satellites are seen from the ground. This question is inspired by space-advertising, a public exhibition in the night sky using a dot matrix of satellites that are bright enough to be seen by the naked eye. Thus, it is important for space advertisement that the specific dot matrix is seen. Moreover, the stability of the dot matrix during a visible span is very valuable. To stabilize the dot matrix, this study formulates an apparent position of a dot from a representative dot seen from the ground. The formulation, linear functions of a set of relative orbital elements, reveals the appearance of the dot matrix. The proposed relative variable in the formulation drives the instability of the dot matrix, thereby revealing an initial stable configuration of deputies from a chief. The arbitrary dot matrix designed using the configuration is stable even at low elevations without orbital control during the visible span.

关键词： formation flying relative motion stabilization astrodynamics multi-apparent motions space advertisement

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