In this paper,the problem of brake orbits with minimal period estimates are considered for the first-order Hamiltonian systems with anisotropic growth,i.e.,the Hamiltonian functions may have super-quadratic,sub-quadra...In this paper,the problem of brake orbits with minimal period estimates are considered for the first-order Hamiltonian systems with anisotropic growth,i.e.,the Hamiltonian functions may have super-quadratic,sub-quadratic and quadratic behaviors simultaneously in different variable components.展开更多
It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cy...It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cylinder.By constructing a bounded solution of the monotone recurrence relation,the main conclusion in this paper is acquired:The induced homeomorphism has Birkhoff orbits provided there is a compact forward-invariant set.Therefore,it generalizes Angenent's results in low-dimensional cases.展开更多
In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions betwee...In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions between rendezvous spacecraft and the target.Lawden’s primer vector theory is then applied on this linear but time-varying system.The analytical solution of the required primer vector for this problem is then derived by using a recently developed method.For the existing non-optimal solutions which don’t satisfy the conditions,the methods are further designed to improve the performance by shifting impulses or adding a new one.Finally,two algorithms are developed for free-impulse time-fixed rendezvous problems.The first algorithm can determine the globally optimal trajectory with the optimal number of impulses.The second one enables for fast trajectory planning.The proposed algorithms have been successfully applied to coplanar and three-dimensional rendezvous problems in which the target is flying on highly elliptical orbits.展开更多
A graph G is said to be super-connected or simply super-κ, if each minimum vertex cut of G isolates a vertex. A graph G is said to be a k-vertex-orbit graph if there are k vertex orbits when Aut(G) acts on V(G). A gr...A graph G is said to be super-connected or simply super-κ, if each minimum vertex cut of G isolates a vertex. A graph G is said to be a k-vertex-orbit graph if there are k vertex orbits when Aut(G) acts on V(G). A graph G is said to be a k-edge-orbit graph if there are k edge orbits when Aut(G) acts on edge set E(G). In this paper, we give a necessary and sufficient condition for connected bipartite 2-vertex-orbit graphs to be super-κ. For 2-edge-orbit graphs,we give a sufficient condition for connected 2-edge-orbit graphs to be super-κ. In addition, we show that if G is a k-regular connected irreducible Ⅱ-kind 2-edge-orbit graph with k ≤ 6 and girth g(G) ≥ 6, or G is a k-regular connected irreducible Ⅲ-kind 2-edge-orbit graph with k ≤ 6and girth g(G) ≥ 8, then G is super-connected.展开更多
We analyze the periodic orbits, quasi periodic orbits and chaotic orbits in the photo gravitational Sun-Saturn system incorporating actual oblateness of Saturn in the planar circular restricted three body problem. In ...We analyze the periodic orbits, quasi periodic orbits and chaotic orbits in the photo gravitational Sun-Saturn system incorporating actual oblateness of Saturn in the planar circular restricted three body problem. In this paper, we study the effect of solar radiation pressure on the location of Sun centered and Saturn centered orbits, its diameter, semi major axis and eccentricity by taking different values of solar radiation pressure q and different values of Jacobi constant “C”, and by considering actual oblateness of Saturn using Poincare surface of section (PSS) method. It is ob-served that by the introduction of perturbing force due to solar radiation pressure admissible range of Jacobi constant C decreases, it is also observed that as value of C decreases the number of islands decreases and as a result the number of periodic and quasi periodic orbits decreases.Fur-ther, the periodic orbits around Saturn and Sun moves towards Sun by decreasing perturbation due to solar radiation pressure q for a specific choice of Jacobi constant C. It is also observed that due to solar radiation pressure, semi major axis and eccentricity of Sun centered periodic orbit reduces, whereas, due to solar radiation pressure uniform change in semi major axis and eccen-tricity of Saturn centered periodic orbits is observed.展开更多
We analyze the periodic orbits of “f” family (simply symmetric retrograde periodic orbits) and the regions of quasi-periodic motion around Saturn in the photo gravitational Sun-Saturn system in the framework of plan...We analyze the periodic orbits of “f” family (simply symmetric retrograde periodic orbits) and the regions of quasi-periodic motion around Saturn in the photo gravitational Sun-Saturn system in the framework of planar circular restricted three-body problem with oblateness. The location, nature and size of these orbits are studied using the numerical technique of Poincare surface of sections (PSS). In this paper we analyze these orbits for different solar radiation pressure (q) and actual oblateness coefficient of Sun Saturn system. It is observed that as Jacobi constant (C) increases, the number of islands in the PSS and consequently the number of periodic and quasi-periodic orbits increase. The periodic orbits around Saturn move towards the Sun with decrease in solar radiation pressure for given value of “C”. It is observed that as the perturbation due to solar radiation pressure decreases, the two separatrices come closer to each other and also come closer to Saturn. It is found that the eccentricity and semi major axis of periodic orbits at both separatrices are increased by perturbation due to solar radiation pressure.展开更多
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...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 dependent.It is shown that the system can be made persistent under some appropriate conditions.Moreover,sufficient conditions that guarantee the existence of a unique positive periodic orbit which is globally asymptotic stable are derived.展开更多
Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analy...Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO missions.However,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 trajectories.In this paper,a novel approach is proposed to construct the analytical solution of bounded close relative motion on DROs.The linear dynamics of relative motion on DRO is established at first.The preliminary forms of the general solutions are obtained based on the Floquet theory.And 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 detail.In each mode,the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier series.In this way,the analytical bounded relative motion on DRO is obtained.Based on the analytical expression,the characteristics of different modes are comprehensively analyzed.The 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 docking.On the basis of quasi-periodic modes,quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per period.The fly-around formation can support observations to targets on DRO from multiple viewing angles.And the fly-around formation is validated in a more practical ephemeris model.展开更多
The electron movement based on the multi-photon nonlinear Compton scattering with the extra-intense stationary laser field is discussed by using KMR (Kroll-Morton-Rosenbluth) theory.We find that there exists only an e...The electron movement based on the multi-photon nonlinear Compton scattering with the extra-intense stationary laser field is discussed by using KMR (Kroll-Morton-Rosenbluth) theory.We find that there exists only an evolution from periodicity to non-periodicity of the un-captured electron phase orbits after the energy exchange between the electron beam and laser fields.With the increase of the absorbed photon number n by an electron, this evolution will be more and more faster, while it is rapidly decreased with the enhancement of the collision non-flexibility ξ of the electrons and photons; When the electrons are captured by the laser fields, the evolution is finished, the electrons will stably transport,and the photons dont give up the energy to these electrons.展开更多
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 ...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.展开更多
The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neit...The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neither a quadratic form in x nor periodic in t and W（t, x） is superquadratic in x.展开更多
Traditional "magic numbers" were once regarded as immutable throughout the nuclear chart. However, unexpected changes were found for unstable nuclei around N = 20. With both proton and neutron numbers around...Traditional "magic numbers" were once regarded as immutable throughout the nuclear chart. However, unexpected changes were found for unstable nuclei around N = 20. With both proton and neutron numbers around the magic number of 20, the neutron-rich ^(39)Cl isotope provides a good test case for the study of the quantumstate evolution across the major shell. In the present work, the negative parity states in ^(39)Cl are investigated through the β decay spectroscopy of 39 S. Newly observed γ transitions together with a new state are assigned into the level scheme of ^(39)Cl. The spin parity of 5/2^- for the lowest negative parity state in ^(39)Cl is reconfirmed using the combined γ transition information. These systematic observations of the negative parity states in ^(39)Cl allow a comprehensive comparison with the theoretical descriptions. The lowest 5/2^- state in ^(39)Cl remains exotic in terms of comparisons with existing theoretical calculations and with the neighboring isotopes having similar single-particle configurations. Further experimental and theoretical investigations are suggested.展开更多
High-specific-impulse electric propulsion technology is promising for future space robotic debris removal in sun-synchronous orbits.Such a prospect involves solving a class of challenging problems of low-thrust orbita...High-specific-impulse electric propulsion technology is promising for future space robotic debris removal in sun-synchronous orbits.Such a prospect involves solving a class of challenging problems of low-thrust orbital rendezvous between an active spacecraft and a free-flying debris.This study focuses on computing optimal low-thrust minimum-time many-revolution trajectories,considering the effects of the Earth oblateness perturbations and null thrust in Earth shadow.Firstly,a set of mean-element orbital dynamic equations of a chaser(spacecraft)and a target(debris)are derived by using the orbital averaging technique,and specifically a slow-changing state of the mean longitude difference is proposed to accommodate to the rendezvous problem.Subsequently,the corresponding optimal control problem is formulated based on the mean elements and their associated costate variables in terms of Pontryagin’s maximum principle,and a practical optimization procedure is adopted to find the specific initial costate variables,wherein the necessary conditions of the optimal solutions are all satisfied.Afterwards,the optimal control profile obtained in mean elements is then mapped into the counterpart that is employed by the osculating orbital dynamics.A simple correction strategy about the initialization of the mean elements,specifically the differential mean true longitude,is suggested,which is capable of minimizing the terminal orbital rendezvous errors for propagating orbital dynamics expressed by both mean and osculating elements.Finally,numerical examples are presented,and specifically,the terminal orbital rendezvous accuracy is verified by solving hundreds of rendezvous problems,demonstrating the effectiveness of the optimization method proposed in this article.展开更多
The authors consider the billiard system with finitely many convex scatters with smooth boundary satisfying the visibility assumption on the plane and prove that the closed orbits for the billiard flow is uniformly di...The authors consider the billiard system with finitely many convex scatters with smooth boundary satisfying the visibility assumption on the plane and prove that the closed orbits for the billiard flow is uniformly distributed.展开更多
This work focuses on how to maintain a high-energy orbit motion of a bistable oscillator when subjected to a low level excitation. An elastic magnifier （EM） positioned between the base and the bistable oscillator is...This work focuses on how to maintain a high-energy orbit motion of a bistable oscillator when subjected to a low level excitation. An elastic magnifier （EM） positioned between the base and the bistable oscillator is used to magnify the base vibration displacement to significantly enhance the output characteristics of the bistable oscillator. The dimensionless electromechanical equations of the bistable oscillator with an EM are derived, and the effects of the mass and stiffness ratios between the EM and the bistable oscillator on the output displacement are studied. It is shown that the jump phenomenon occurs at a lower excitation level with increasing the mass and stiffness ratios. With the comparison of the displacement trajectories and the phase portraits obtained from experiments, it is vMidated that the bistable oscillator with an EM can effectively oscillate in a high-energy orbit and can generate a superior output vibration at a low excitation level as compared with the bistable oscillator without an EM.展开更多
An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator...An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator and denominator of Pad′e approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Pad′e approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Pad′e approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Pad′e approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method.展开更多
One-sided ascending or descending Synthetic Aperture Radar（SAR） stereoradargrammetry has limited accuracy of topographic mapping due to the short spatial baseline（-100 km） and small intersection angle. In order to...One-sided ascending or descending Synthetic Aperture Radar（SAR） stereoradargrammetry has limited accuracy of topographic mapping due to the short spatial baseline（-100 km） and small intersection angle. In order to improve the performance and reliability of generating digital elevation model（DEM） from spaceborne SAR radargrammetry, an exploration of two-sided stereoradargrammetry from the combination of ascending and descending orbits with geometric configuration of long spatial baseline（-1000 km） was conducted in this study. The slant-range geometry between SAR sensors to the earth surface and the Doppler positioning equations were employed to establish the stereoscopic intersection model. The measurement uncertainty of two-sided radargrammetric elevation was estimated on the basis of radar parallax of homogeneous points between input SAR images. Two stereo-pairs of ALOS/PALSAR（Advanced Land Observing Satellite/Phased Array type L-band Synthetic Aperture Radar） acquisitions with the orbital separation almost 1080 km over the west Sichuan foreland basin with rolling topography in southwestern China were employed in the study to obtain the up-to-date terrain data after the 2008 Wenchuan earthquake that hit this area. Thequantitative accuracy assessment of two-sided radargrammetric DEM was performed with reference to field GPS observations. The experimental results show that the elevation accuracy reaches 5.5 m without ground control points（GCPs） used, and the accuracy is further improved to 1.5 m with only one GPS GCP used as the least constraint. The theoretical analysis and testing results demonstrate that the twosided long baseline SAR radargrammetry from the ascending and descending orbits can be a very promising technical alternative for large-area and high accuracy topographic mapping.展开更多
The evolution of the electron phase orbits based on the multi-photon nonlinear Compton scattering with the high power laser-plasma is discussed by using Kroll-Morton-Rosenbluth theory. The random evolution of the un-c...The evolution of the electron phase orbits based on the multi-photon nonlinear Compton scattering with the high power laser-plasma is discussed by using Kroll-Morton-Rosenbluth theory. The random evolution of the un-captured electron phase orbits from periodicity to non-periodicity is found after the energy has been exchanged between the electron and photons. With the increase of the absorbed photon number n by an electron,this evolution will be more and more intense, while which is rapidly decreased with the enhancement of the collision non-flexibility ξ and their initial speeds of the electrons and photons,but this evolution is lower than that in the high power laser field. When the electrons are captured by the laser field,the evolution is finished,and the electrons will stably transport,and the photons don’t provide the energy for these electrons any more.展开更多
This study investigates the problem of areostationary orbits around Mars in three-dimensional space. Areostationary orbits are expected to be used to establish a future telecommunication network for the exploration of...This study investigates the problem of areostationary orbits around Mars in three-dimensional space. Areostationary orbits are expected to be used to establish a future telecommunication network for the exploration of Mars. However, no artificial satellites have been placed in these orbits thus far. The characteristics of the Martian gravity field are presented, and areostationary points and their linear stability are cal- culated. By taking linearized solutions in the planar case as the initial guesses and utilizing the Levenberg-Marquardt method, families of periodic orbits around areo- stationary points are shown to exist. Short-period orbits and long-period orbits are found around linearly stable areostationary points, but only short-period orbits are found around unstable areostationary points. Vertical periodic orbits around both lin- early stable and unstable areostationary points are also examined. Satellites in these periodic orbits could depart from areostationary points by a few degrees in longitude, which would facilitate observation of the Martian topography. Based on the eigenval- ues of the monodromy matrix, the evolution of the stability index of periodic orbits is determined. Finally, heteroclinic orbits connecting the two unstable areostationary points are found, providing the possibility for orbital transfer with minimal energy consumption.展开更多
This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primar...This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. Both the terms due to oblateness of the smaller primary are considered. Numerical as well as analytical solutions are obtained around the Lagrangian point L1, which lies between the primaries, of the Sun-Earth system. A comparison with the real time flight data of SOHO mission is made. Inclusion of oblateness of the smaller primary can improve the accuracy. Due to the effect of radiation pressure and oblateness, the size and the orbital period of the halo orbit around L1 are found to increase.展开更多
基金supported by the NSFC(12301138)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(2021L377)+1 种基金the Doctoral Scientific Research Foundation of Shanxi Datong University(2018-B-15)The second author’s work was supported by the NSFC(12171108).
文摘In this paper,the problem of brake orbits with minimal period estimates are considered for the first-order Hamiltonian systems with anisotropic growth,i.e.,the Hamiltonian functions may have super-quadratic,sub-quadratic and quadratic behaviors simultaneously in different variable components.
基金Supported by the National Natural Science Foundation of China(12201446)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(22KJB110005)the Shuangchuang Program of Jiangsu Province(JSSCBS20220898)。
文摘It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cylinder.By constructing a bounded solution of the monotone recurrence relation,the main conclusion in this paper is acquired:The induced homeomorphism has Birkhoff orbits provided there is a compact forward-invariant set.Therefore,it generalizes Angenent's results in low-dimensional cases.
基金supported by National Natural Science Foundation of China(No.12172288)National Key Basic Research Program of China:Gravitational Wave Detection Project(Nos.2021YFC2202601 and 2021YFC2202603)General Program of Natural Science Foundation of Higher Education of Jiangsu Province(No.21KJB590001)。
文摘In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions between rendezvous spacecraft and the target.Lawden’s primer vector theory is then applied on this linear but time-varying system.The analytical solution of the required primer vector for this problem is then derived by using a recently developed method.For the existing non-optimal solutions which don’t satisfy the conditions,the methods are further designed to improve the performance by shifting impulses or adding a new one.Finally,two algorithms are developed for free-impulse time-fixed rendezvous problems.The first algorithm can determine the globally optimal trajectory with the optimal number of impulses.The second one enables for fast trajectory planning.The proposed algorithms have been successfully applied to coplanar and three-dimensional rendezvous problems in which the target is flying on highly elliptical orbits.
基金Supported by the National Natural Science Foundation of Xinjiang(2020D04046)the National Natural Science Foundation of Shanxi(20210302123097)the National Natural Science Foundation of China(12371356,11961067).
文摘A graph G is said to be super-connected or simply super-κ, if each minimum vertex cut of G isolates a vertex. A graph G is said to be a k-vertex-orbit graph if there are k vertex orbits when Aut(G) acts on V(G). A graph G is said to be a k-edge-orbit graph if there are k edge orbits when Aut(G) acts on edge set E(G). In this paper, we give a necessary and sufficient condition for connected bipartite 2-vertex-orbit graphs to be super-κ. For 2-edge-orbit graphs,we give a sufficient condition for connected 2-edge-orbit graphs to be super-κ. In addition, we show that if G is a k-regular connected irreducible Ⅱ-kind 2-edge-orbit graph with k ≤ 6 and girth g(G) ≥ 6, or G is a k-regular connected irreducible Ⅲ-kind 2-edge-orbit graph with k ≤ 6and girth g(G) ≥ 8, then G is super-connected.
文摘We analyze the periodic orbits, quasi periodic orbits and chaotic orbits in the photo gravitational Sun-Saturn system incorporating actual oblateness of Saturn in the planar circular restricted three body problem. In this paper, we study the effect of solar radiation pressure on the location of Sun centered and Saturn centered orbits, its diameter, semi major axis and eccentricity by taking different values of solar radiation pressure q and different values of Jacobi constant “C”, and by considering actual oblateness of Saturn using Poincare surface of section (PSS) method. It is ob-served that by the introduction of perturbing force due to solar radiation pressure admissible range of Jacobi constant C decreases, it is also observed that as value of C decreases the number of islands decreases and as a result the number of periodic and quasi periodic orbits decreases.Fur-ther, the periodic orbits around Saturn and Sun moves towards Sun by decreasing perturbation due to solar radiation pressure q for a specific choice of Jacobi constant C. It is also observed that due to solar radiation pressure, semi major axis and eccentricity of Sun centered periodic orbit reduces, whereas, due to solar radiation pressure uniform change in semi major axis and eccen-tricity of Saturn centered periodic orbits is observed.
文摘We analyze the periodic orbits of “f” family (simply symmetric retrograde periodic orbits) and the regions of quasi-periodic motion around Saturn in the photo gravitational Sun-Saturn system in the framework of planar circular restricted three-body problem with oblateness. The location, nature and size of these orbits are studied using the numerical technique of Poincare surface of sections (PSS). In this paper we analyze these orbits for different solar radiation pressure (q) and actual oblateness coefficient of Sun Saturn system. It is observed that as Jacobi constant (C) increases, the number of islands in the PSS and consequently the number of periodic and quasi-periodic orbits increase. The periodic orbits around Saturn move towards the Sun with decrease in solar radiation pressure for given value of “C”. It is observed that as the perturbation due to solar radiation pressure decreases, the two separatrices come closer to each other and also come closer to Saturn. It is found that the eccentricity and semi major axis of periodic orbits at both separatrices are increased by perturbation due to solar radiation pressure.
基金the Start- up foundation of Fuzhou University ( 0 0 30 82 4 2 2 8),the Foundation ofDeveloping Science and Technical Developmentof Fuzhou University ( 2 0 0 3- QX- 2 1 ) and the Foundation ofScience and Technology of Fujian Province of PR China for Young
文摘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 dependent.It is shown that the system can be made persistent under some appropriate conditions.Moreover,sufficient conditions that guarantee the existence of a unique positive periodic orbit which is globally asymptotic stable are derived.
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDA30010200)。
文摘Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO missions.However,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 trajectories.In this paper,a novel approach is proposed to construct the analytical solution of bounded close relative motion on DROs.The linear dynamics of relative motion on DRO is established at first.The preliminary forms of the general solutions are obtained based on the Floquet theory.And 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 detail.In each mode,the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier series.In this way,the analytical bounded relative motion on DRO is obtained.Based on the analytical expression,the characteristics of different modes are comprehensively analyzed.The 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 docking.On the basis of quasi-periodic modes,quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per period.The fly-around formation can support observations to targets on DRO from multiple viewing angles.And the fly-around formation is validated in a more practical ephemeris model.
文摘The electron movement based on the multi-photon nonlinear Compton scattering with the extra-intense stationary laser field is discussed by using KMR (Kroll-Morton-Rosenbluth) theory.We find that there exists only an evolution from periodicity to non-periodicity of the un-captured electron phase orbits after the energy exchange between the electron beam and laser fields.With the increase of the absorbed photon number n by an electron, this evolution will be more and more faster, while it is rapidly decreased with the enhancement of the collision non-flexibility ξ of the electrons and photons; When the electrons are captured by the laser fields, the evolution is finished, the electrons will stably transport,and the photons dont give up the energy to these electrons.
文摘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.
基金Supported by National Natural Science Foundation of China (10771173)
文摘The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neither a quadratic form in x nor periodic in t and W（t, x） is superquadratic in x.
基金Supported by JSPS and CNRS under the Japan-France Research Cooperative Programthe Grant-in-Aid for Scientific Research on Innovative Areas"Toward new frontiers:Encounter and synergy of state-of-the-art astronomical detectors and exotic quantum beams",JSPS/MEXT KAKENHI under Grant Nos JP18HO3692 and JP18H05462+1 种基金the National Key R&D Program of China(2018YFA0404403)the National Natural Science Foundation of China Nos 11775316,11535004,11875074 and 11875073
文摘Traditional "magic numbers" were once regarded as immutable throughout the nuclear chart. However, unexpected changes were found for unstable nuclei around N = 20. With both proton and neutron numbers around the magic number of 20, the neutron-rich ^(39)Cl isotope provides a good test case for the study of the quantumstate evolution across the major shell. In the present work, the negative parity states in ^(39)Cl are investigated through the β decay spectroscopy of 39 S. Newly observed γ transitions together with a new state are assigned into the level scheme of ^(39)Cl. The spin parity of 5/2^- for the lowest negative parity state in ^(39)Cl is reconfirmed using the combined γ transition information. These systematic observations of the negative parity states in ^(39)Cl allow a comprehensive comparison with the theoretical descriptions. The lowest 5/2^- state in ^(39)Cl remains exotic in terms of comparisons with existing theoretical calculations and with the neighboring isotopes having similar single-particle configurations. Further experimental and theoretical investigations are suggested.
基金supported by the National Key Research and Development Project(Grant No.2018YFB1900605)the Key Research Program of Chinese Academy of Sciences(Grant No.ZDRW-KT-2019-1).
文摘High-specific-impulse electric propulsion technology is promising for future space robotic debris removal in sun-synchronous orbits.Such a prospect involves solving a class of challenging problems of low-thrust orbital rendezvous between an active spacecraft and a free-flying debris.This study focuses on computing optimal low-thrust minimum-time many-revolution trajectories,considering the effects of the Earth oblateness perturbations and null thrust in Earth shadow.Firstly,a set of mean-element orbital dynamic equations of a chaser(spacecraft)and a target(debris)are derived by using the orbital averaging technique,and specifically a slow-changing state of the mean longitude difference is proposed to accommodate to the rendezvous problem.Subsequently,the corresponding optimal control problem is formulated based on the mean elements and their associated costate variables in terms of Pontryagin’s maximum principle,and a practical optimization procedure is adopted to find the specific initial costate variables,wherein the necessary conditions of the optimal solutions are all satisfied.Afterwards,the optimal control profile obtained in mean elements is then mapped into the counterpart that is employed by the osculating orbital dynamics.A simple correction strategy about the initialization of the mean elements,specifically the differential mean true longitude,is suggested,which is capable of minimizing the terminal orbital rendezvous errors for propagating orbital dynamics expressed by both mean and osculating elements.Finally,numerical examples are presented,and specifically,the terminal orbital rendezvous accuracy is verified by solving hundreds of rendezvous problems,demonstrating the effectiveness of the optimization method proposed in this article.
基金This work is supported by the National Natural Science Foundation of China(10571174)
文摘The authors consider the billiard system with finitely many convex scatters with smooth boundary satisfying the visibility assumption on the plane and prove that the closed orbits for the billiard flow is uniformly distributed.
基金Supported by the National Natural Science Foundation of China under Grant No 51277165the Natural Science Foundation of Zhejiang Province under Grant No LY15F10001
文摘This work focuses on how to maintain a high-energy orbit motion of a bistable oscillator when subjected to a low level excitation. An elastic magnifier （EM） positioned between the base and the bistable oscillator is used to magnify the base vibration displacement to significantly enhance the output characteristics of the bistable oscillator. The dimensionless electromechanical equations of the bistable oscillator with an EM are derived, and the effects of the mass and stiffness ratios between the EM and the bistable oscillator on the output displacement are studied. It is shown that the jump phenomenon occurs at a lower excitation level with increasing the mass and stiffness ratios. With the comparison of the displacement trajectories and the phase portraits obtained from experiments, it is vMidated that the bistable oscillator with an EM can effectively oscillate in a high-energy orbit and can generate a superior output vibration at a low excitation level as compared with the bistable oscillator without an EM.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11172093 and 11372102)the Hunan Provincial Innovation Foundation for Postgraduate,China(Grant No.CX2012B159)
文摘An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator and denominator of Pad′e approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Pad′e approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Pad′e approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Pad′e approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method.
基金supported by the National Natural Science Foundation of China(Grant Nos.41472255,51178404)Open Research Fund by Sichuan Engineering Research Center for Emergency Mapping & Disaster Reduction(Program K2014B006)Fundamental Research Funds for the Central Universities(Grant Nos.SWJTU12ZT07,2682014BR014)
文摘One-sided ascending or descending Synthetic Aperture Radar（SAR） stereoradargrammetry has limited accuracy of topographic mapping due to the short spatial baseline（-100 km） and small intersection angle. In order to improve the performance and reliability of generating digital elevation model（DEM） from spaceborne SAR radargrammetry, an exploration of two-sided stereoradargrammetry from the combination of ascending and descending orbits with geometric configuration of long spatial baseline（-1000 km） was conducted in this study. The slant-range geometry between SAR sensors to the earth surface and the Doppler positioning equations were employed to establish the stereoscopic intersection model. The measurement uncertainty of two-sided radargrammetric elevation was estimated on the basis of radar parallax of homogeneous points between input SAR images. Two stereo-pairs of ALOS/PALSAR（Advanced Land Observing Satellite/Phased Array type L-band Synthetic Aperture Radar） acquisitions with the orbital separation almost 1080 km over the west Sichuan foreland basin with rolling topography in southwestern China were employed in the study to obtain the up-to-date terrain data after the 2008 Wenchuan earthquake that hit this area. Thequantitative accuracy assessment of two-sided radargrammetric DEM was performed with reference to field GPS observations. The experimental results show that the elevation accuracy reaches 5.5 m without ground control points（GCPs） used, and the accuracy is further improved to 1.5 m with only one GPS GCP used as the least constraint. The theoretical analysis and testing results demonstrate that the twosided long baseline SAR radargrammetry from the ascending and descending orbits can be a very promising technical alternative for large-area and high accuracy topographic mapping.
基金Natural Science Basic Research Project for Education Department of Henan Province(20011400006)
文摘The evolution of the electron phase orbits based on the multi-photon nonlinear Compton scattering with the high power laser-plasma is discussed by using Kroll-Morton-Rosenbluth theory. The random evolution of the un-captured electron phase orbits from periodicity to non-periodicity is found after the energy has been exchanged between the electron and photons. With the increase of the absorbed photon number n by an electron,this evolution will be more and more intense, while which is rapidly decreased with the enhancement of the collision non-flexibility ξ and their initial speeds of the electrons and photons,but this evolution is lower than that in the high power laser field. When the electrons are captured by the laser field,the evolution is finished,and the electrons will stably transport,and the photons don’t provide the energy for these electrons any more.
基金supported by the National Basic Research Program of China (973 Program,No.2012CB720000)the National Natural Science Foundation of China(Grant No.11072122)
文摘This study investigates the problem of areostationary orbits around Mars in three-dimensional space. Areostationary orbits are expected to be used to establish a future telecommunication network for the exploration of Mars. However, no artificial satellites have been placed in these orbits thus far. The characteristics of the Martian gravity field are presented, and areostationary points and their linear stability are cal- culated. By taking linearized solutions in the planar case as the initial guesses and utilizing the Levenberg-Marquardt method, families of periodic orbits around areo- stationary points are shown to exist. Short-period orbits and long-period orbits are found around linearly stable areostationary points, but only short-period orbits are found around unstable areostationary points. Vertical periodic orbits around both lin- early stable and unstable areostationary points are also examined. Satellites in these periodic orbits could depart from areostationary points by a few degrees in longitude, which would facilitate observation of the Martian topography. Based on the eigenval- ues of the monodromy matrix, the evolution of the stability index of periodic orbits is determined. Finally, heteroclinic orbits connecting the two unstable areostationary points are found, providing the possibility for orbital transfer with minimal energy consumption.
文摘This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. Both the terms due to oblateness of the smaller primary are considered. Numerical as well as analytical solutions are obtained around the Lagrangian point L1, which lies between the primaries, of the Sun-Earth system. A comparison with the real time flight data of SOHO mission is made. Inclusion of oblateness of the smaller primary can improve the accuracy. Due to the effect of radiation pressure and oblateness, the size and the orbital period of the halo orbit around L1 are found to increase.
