The dynamics of fluid and non-buoyant particles in a librating horizontal annulus is studied experimentally.In the absence of librations,the granular material forms a cylindrical layer near the outer boundary of the a...The dynamics of fluid and non-buoyant particles in a librating horizontal annulus is studied experimentally.In the absence of librations,the granular material forms a cylindrical layer near the outer boundary of the annulus and undergoes rigid-body rotation with the fluid and the annulus.It is demonstrated that the librational liquefaction of the granular material results in pattern formation.This self-organization process stems from the excitation of inertial modes induced by the oscillatory motion of liquefied granular material under the influence of the gravitational force.The inertial wave induces vortical fluid flow which entrains particles from rest and forms eroded areas that are equidistant from each other along the axis of rotation.Theoretical analysis and experiments demonstrate that a liquefied layer of granular material oscillates with a radian frequency equal to the angular velocity of the annulus and interacts with the inertial wave it excites.The new phenomenon of libration-induced pattern formation is of practical interest as it can be used to control multiphase flows and mass transfer in rotating containers in a variety of industrial processes.展开更多
This paper proposed a new libration decoupling analytical speed function(LD-ASF)in lieu of the classic analytical speed function to control the climber's speed along a partial space elevator to improve libration s...This paper proposed a new libration decoupling analytical speed function(LD-ASF)in lieu of the classic analytical speed function to control the climber's speed along a partial space elevator to improve libration stability in cargo transportation.The LD-ASF is further optimized for payload transportation efficiency by a novel coordinate game theory to balance competing control objectives among payload transport speed,stable end body's libration,and overall control input via model predictive control.The transfer period is divided into several sections to reduce computational burden.The validity and efficacy of the proposed LD-ASF and coordinate game-based model predictive control are demonstrated by computer simulation.Numerical results reveal that the optimized LD-ASF results in higher transportation speed,stable end body's libration,lower thrust fuel consumption,and more flexible optimization space than the classic analytical speed function.展开更多
Ⅰ. INTRODUCTIONBesides the theoretical meaning of determining the flee librations itself, we may also infer the excitation and dissipation mechanisms, such as meteorite impact, moonquakes and turbulent core-mantle fr...Ⅰ. INTRODUCTIONBesides the theoretical meaning of determining the flee librations itself, we may also infer the excitation and dissipation mechanisms, such as meteorite impact, moonquakes and turbulent core-mantle frictions. Therefore, it will be of great significance to realize the origins, evolutions and structures of the bodies in the solar system.展开更多
The study of average convection in a rotating cavity subjected to modulated rotation is an interesting area for the development of both fundamental and applied science.This phenomenon finds application in the field of...The study of average convection in a rotating cavity subjected to modulated rotation is an interesting area for the development of both fundamental and applied science.This phenomenon finds application in the field of mass transfer and fluid flow control,relevant examples being crystal growth under reduced gravity and fluid mixing in microfluidic devices for cell cultures.In this study,the averaged flow generated by the oscillating motion of a fluid in a planar layer rotating about a horizontal axis is experimentally investigated.The boundaries of the layer are maintained at constant temperatures,while the lateral cylindrical wall is thermally insulated.It is demonstrated that libration results in intense oscillatory fluid motion,which in turn produces a time-averaged flow.For the first time,quantitative measures for the instantaneous velocity field are obtained using the Particle Image Velocimetry technique.It is revealed that the flow has the form of counter-rotating vortices.The vortex circulations sense changes during a libration cycle.An increase in the rotation rate and amplitude of the cavity libration results in an increase in the flow intensity.The heat transfer and time-averaged velocity are examined accordingly as a function of the dimensionless oscillation frequency,and resonant excitation of heat transfer and average oscillation velocity are revealed.The threshold curve for the onset of the averaged convection is identified in the plane of control parameters(dimensionless rotational velocity and pulsation Reynolds number).It is found that an increase in the dimensionless rotational velocity has a stabilizing effect on the onset of convection.展开更多
For mitigating the libration angle fluctuation of the tethered satellite system,this paper discusses how to make the uniform velocity-deceleration separation scheme achieve the best effect.First,a judgment condition i...For mitigating the libration angle fluctuation of the tethered satellite system,this paper discusses how to make the uniform velocity-deceleration separation scheme achieve the best effect.First,a judgment condition is established to determine the tether state by comparing the tether length and the relative distance of the sub-satellite and the parent satellite.Based on the tethered satellite system dynamics equation and Clohessy-Wiltshire equation,dynamic models are given for four cases of tether states.Second,the influence of the uniform velocity-deceleration separation scheme on the libration angle is analyzed by taking the libration angle at the separation ending time and the mean absolute value of the libration angle as index functions.Then,the optimality problem of the uniform velocity-deceleration separation scheme is formulated as an optimization problem with constraints,and an approximate solution algorithm is given by combining the back propagation neural network and Newton-Raphson method of multiple initial values.Finally,the effectiveness of the proposed method is verified by a numerical simulation.展开更多
This article addresses the design of the trajectory transferring from Earth to Halo orbit, and proposes a timing closed-loop strategy of correction maneuver during the transfer in the frame of circular restricted thre...This article addresses the design of the trajectory transferring from Earth to Halo orbit, and proposes a timing closed-loop strategy of correction maneuver during the transfer in the frame of circular restricted three body problem （CR3BP）. The relation between the Floquet multipliers and the magnitudes of Halo orbit is established, so that the suitable magnitude for the aerospace mission is chosen in terms of the stability of Halo orbit. The stable manifold is investigated from the Poincar6 mapping defined which is different from the previous researches, and six types of single-impulse transfer trajectories are attained from the geometry of the invariant manifolds. Based on one of the trajectories of indirect transfer which are ignored in the most of literatures, the stochastic control theory for imperfect information of the discrete linear stochastic system is applied to design the trajectory correction maneuver. The statistical dispersion analysis is performed by Monte-Carlo simulation,展开更多
The Moon’s physical librations have been extensively studied, and elaborate researches have been developed for the purpose of deriving accurate modes of free librations. Our motivation comes from the Planetary and Lu...The Moon’s physical librations have been extensively studied, and elaborate researches have been developed for the purpose of deriving accurate modes of free librations. Our motivation comes from the Planetary and Lunar Ephemeris DE430 by JPL/NASA, which was created in April 2013,and is reported to be the most accurate lunar ephemeris today using the data from Gravity Recovery and Interior Laboratory（GRAIL）. Therefore, the residuals after fitting the model have reduced owing to improvement in the libration models, and the free librations embedded in the Euler angles have also improved. We use Fourier analysis to extract the approximate frequencies from DE430 and then a quadratic interpolation method is used to determine higher accuracy frequencies. With the frequencies,the linear least-squares fitting method is employed to fit the lunar physical librations to DE430. From this analysis we identified the three modes of free physical librations, and estimated the amplitudes as 1.471′′in longitude, 0.025′′in latitude and 8.19′′× 3.31′′for the wobble, with the respective periods of1056.16, 8806.9 and 27262.99 d. Since the free librations damp with time, they require recent excitation or a continuous stimulating mechanism in order to sustain.展开更多
Libration-point missions have been very useful and successful. Due to the unstable natures of most of these orbits, the long-time stationkeeping demands frequent maneuvers and precise orbit determinations. Earth-based...Libration-point missions have been very useful and successful. Due to the unstable natures of most of these orbits, the long-time stationkeeping demands frequent maneuvers and precise orbit determinations. Earth-based tracking will have to undertake much more responsibilities with the increasing number of libration missions. An autonomous navigation system could offer a better way to decrease the need for Earth-based tracking. Nevertheless, when an autonomous navigation system is applied, there are three important factors affecting autonomous navigation accuracy, i.e., the accuracy of initial conditions, the accuracy of measurements, and the accuracy of onboard dynamics for propagation. This paper focuses on analyzing the influence from the third factor and finding an appropriate navigation dynamics, which can satisfy the requirement of estimation accuracy but not cause too much burden for onboard computation. When considering the restricted three-body model and the bicircular restricted four-body model as navigation dynamics, the astrin- gency is not shown during the simulations. Meanwhile, when considering the influences of the Sun＇s direct and indirect perturbations and the eccentricity of the Moon＇s orbit, a new navigation dynamic model with the standard ephemerides is proposed. The simulation shows the feasibility of the proposed model.展开更多
Flight schemes for the CHANG＇E-5T1 extended mission are investigated in this paper.In the flight scheme and trajectory design, the remaining propellant of the CHANG＇E-5T1 mission is utilized. The CHANG＇E-5T1 missio...Flight schemes for the CHANG＇E-5T1 extended mission are investigated in this paper.In the flight scheme and trajectory design, the remaining propellant of the CHANG＇E-5T1 mission is utilized. The CHANG＇E-5T1 mission is firstly introduced with feasible flight goals derived based on the terminal trajectory and satellite status. The flight schemes are designed to include a lunar return and the libration points in the Sun-Earth/Moon and Earth-Moon systems, with an emphasis on the Earth-Moon triangle libration point thus far unexplored. Secondly, three schemes are proposed for the CHANG＇E-5T1 extended mission with different flight goals. The direct libration point orbit transfer and injection method is adopted to solve the issue in the transfer trajectory design.Furthermore, an innovative concept is proposed to transfer from the Earth-Moon collinear libration point to the triangle point using the Sun-Earth/Moon libration point. Finally, the merits and drawbacks of the three schemes are discussed in terms of flight time, control energy and frequency, flight distance, and goal value. As a result, the scheme including a lunar return and the Earth-Moon L2 libration point is selected for the CHANG＇E-5T1 extended mission. A flight to the Earth-Moon libration point is achieved, replicating the achievement of the ARTEMIS mission.展开更多
This paper studies the libration and stabilization of a parallel partial space elevator system in circular orbits. The system is made up of two paralleled partial space elevators, each of which consists of one main sa...This paper studies the libration and stabilization of a parallel partial space elevator system in circular orbits. The system is made up of two paralleled partial space elevators, each of which consists of one main satellite, one end body and a climber moving along the tether between them.The libration characteristics of the elevator are studied through numerical analysis by a new dynamic model, and a novel control strategy is proposed to stabilize the swing of the end body by projecting the climber speeds only. Optimal control method is used to implement the new control strategy in the case where the climbers move in opposite direction. The simulation results validate the effectiveness of the proposed control strategy whose application will neither sacrifice the transport efficiency nor exacerbate libration significantly.展开更多
An improved numerical method that can construct Halo/Lissajous orbits in the vicinity of collinear libration points in a full solar system model is investigated. A full solar system gravitational model in the geocentr...An improved numerical method that can construct Halo/Lissajous orbits in the vicinity of collinear libration points in a full solar system model is investigated. A full solar system gravitational model in the geocentric rotating coordinate system with a clear presentation of the angular velocity relative to the inertial coordinate system is proposed. An alternative way to determine patch points in the multiple shooting method is provided based on a dynamical analysis with Poincare′sections. By employing the new patch points and sequential quadratic programming, Halo orbits for L1, L2, and L3points as well as Lissajous orbits for L1and L2points in the EarthMoon system are generated with the proposed full solar system gravitational model to verify the effectiveness of the proposed method.展开更多
The phologravilational restricled three-body problem in which the mass reduclionfactors of two primaries q_1 q_2( -∞, 1] are siudied and an analytic meihod toesli,;iale the number of libralion points ana io calculate...The phologravilational restricled three-body problem in which the mass reduclionfactors of two primaries q_1 q_2( -∞, 1] are siudied and an analytic meihod toesli,;iale the number of libralion points ana io calculate lheir hoalion is given in thispaper. The results show lhal in phologravilalional reslricled three-body problem, thenumber of librafion poinis is .from one to seven for different q_1 and q_2. As application,the motion of dust grain like comet tail in the solar syslern is also discussed.展开更多
To carry out the deep space exploration tasks near Sun-Earth Libration point L2, the CRTBP dynamic model was built up and the numerical conditional quasi-periodic orbit （Lissajons orbit） was computed near L2. Then, ...To carry out the deep space exploration tasks near Sun-Earth Libration point L2, the CRTBP dynamic model was built up and the numerical conditional quasi-periodic orbit （Lissajons orbit） was computed near L2. Then, a formation controller was designed with linear matrix inequality to overcome the difficuhy of parameter tuning. To meet the demands of formation accuracy and present thruster＇s capability, a threshold scheme was adopted for formation control. Finally, some numerical simulations and analysis were completed to demonstrate the feasibility of the proposed control strategy.展开更多
This paper aims to provide further study on the nonlinear modeling and controller design of formation flying spacecraft in deep space missions. First, in the Sun-Earth system, the nonlinear formation dynamics for the ...This paper aims to provide further study on the nonlinear modeling and controller design of formation flying spacecraft in deep space missions. First, in the Sun-Earth system, the nonlinear formation dynamics for the circular restricted three-body problem （CRTBP） and elliptic restricted three-body problem （ERTBP） are presented. Then, with the Floquet mode method, an impulsive controller is developed to keep the Chief on the desired Halo orbit. Finally, a nonlinear adaptive control scheme based on Nonzero set- point LQR and neural network is proposed to achieve high precision formation maneuver and keeping. The simulation results indicate that the proposed nonlinear control strategy is reasonable as it considers not only the orbit keeping of the Chief, but also the formation modeling inaccuracy. Moreover, the nonlinear adaptive control scheme is effective to improve the control accuracy of the formation keeping.展开更多
In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semianalytical computation of ...In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semianalytical computation of the center manifolds and the associated canonical transformation are valuable tools for exploring the design space of libration point missions. This paper deals with the refinement of reduction to the center manifold procedure. In order to reduce the amount of calculation needed and avoid repetitive computation of the Poisson bracket, a modified method is presented. By using a polynomial optimization technique, the coordinate transformation is conducted more efficiently. In addition, an alternative way to do the canonical coordinate transformation is discussed, which complements the classical approach. Numerical simulation confirms that more accurate and efficient numerical exploration of the center manifold is made possible by using the refined method.展开更多
Spacecrafts in periodic or quasi-periodic orbits near the collinear libration points are proved to be excellent platforms for scientific investigations of various phenomena.Since such periodic or quasi-periodic orbits...Spacecrafts in periodic or quasi-periodic orbits near the collinear libration points are proved to be excellent platforms for scientific investigations of various phenomena.Since such periodic or quasi-periodic orbits are exponentially unstable,the station-keeping maneuver is needed. A station-keeping strategy which is found by an analytical method is presented to eradicate the dominant unstable component of the libration point trajectories.The inhibit force transforms the unstable component to a stable component.In this method,it is not necessary to determine a nominal orbit as a reference path.展开更多
A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields a...A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields an unstable linear parameter-varying system with periodic coefficients. Given the variational equations, an innovative control law based on characteristic exponent assignment is introduced for libration point orbit maintenance. A numerical simulation choosing the Richardson＇s third order approximation for a halo orbit as a nominal orbit is conducted, and the results demonstrate the effectiveness of this control law.展开更多
To meet the increasing research demand for deep space exploration,especially for the second libration point (L2) conditional periodic orbit (Halo orbit) in the Sun-Earth system,the methods to get analytical Halo orbit...To meet the increasing research demand for deep space exploration,especially for the second libration point (L2) conditional periodic orbit (Halo orbit) in the Sun-Earth system,the methods to get analytical Halo orbit and differential-correction Halo orbit were described firstly,and the corresponding orbits accuracy was analyzed.Then,based on the results of third-order and differential-correction Halo orbits,the formation form was studied.Analysis was carried out to discuss the influence of system amplitude,initial phase,and phase difference on the formation form,as well as that of initial orbit values on form accuracy.Finally,some simulation results demonstrate the validity of the proposed methods.展开更多
In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The...In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The libration points and the corresponding Jacobi constants are obtained with different values of the solar radiation pressure coefficient. The motion and its stability about each point are studied. A family of periodic orbits under the effects of the gravitational forces of the primaries and the solar radiation pressure are obtained depending on the pure numerical method. This purpose is applied to the Sun-Earth-Moon-Space craft system, and the results obtained are in a good agreement with the previous work such as (Kumari and Papadouris, 2013).展开更多
This article believes that ＂Chinese Dream＂ has three dimensions： First, ＂Chinese Dream＂ is the inevitable demands of Chinese reconstruction and it is the deepest desire of Chinese nation since the Chinese modern ...This article believes that ＂Chinese Dream＂ has three dimensions： First, ＂Chinese Dream＂ is the inevitable demands of Chinese reconstruction and it is the deepest desire of Chinese nation since the Chinese modern history. Second, the modernism of socialism with Chinese feature is the process of Chinese modernism. Third, the third theoretical dimension, 1 believe, is the ideal of socialism. I would like to take the film ＂Lost＂ and ＂Peking Monk＂ as examples and analyze the specific form of expression. This article is going to indicate in the end that ＂the revolution of aesthetics＂ and the assignments of critics, which can be recognized as the intuitive ability, could merge the historical affair and the human nature, which literature comprise, together and deliver deeper analyses and appraise The mission of critics is not only to distinctly emerge the aesthetic form of the literal works, but also analyze and seize the ＂aesthetic form＂ of them, that is to say, their mission is to find the aesthetic meanings of aesthetic expression from commonage in order to achieve the goal of leading and stimulating people ensuing the consciousness and liberation of culture. That is the most important mission and responsibility of Marxist literal criticism and literal critics. This is a rather tough task and refers to the new understanding and attitude to the relative questions of literature and culture. In the eyes of some self-complacent intellectuals, the responsibility for literature and critics is the ＂aesthetic entertainment＂ and ＂spiritual redemption＂. The significance of Marxist Aesthetics lies in that it upgrades the general ＂literal principle＂ and ＂aesthetic principle＂ in to a level of social development and national deliverance, and also it regards whether the literature having the function of cultural libration as the more pivotal content. The assignment for the critics and litterateurs is to engage and promote the production and promulgate for this significance, the cultural consciousness and liberation.展开更多
基金funded by the Ministry of Education of the Russian Federation within the framework of a state assignment,number 1023032300071-6-2.3.1.
文摘The dynamics of fluid and non-buoyant particles in a librating horizontal annulus is studied experimentally.In the absence of librations,the granular material forms a cylindrical layer near the outer boundary of the annulus and undergoes rigid-body rotation with the fluid and the annulus.It is demonstrated that the librational liquefaction of the granular material results in pattern formation.This self-organization process stems from the excitation of inertial modes induced by the oscillatory motion of liquefied granular material under the influence of the gravitational force.The inertial wave induces vortical fluid flow which entrains particles from rest and forms eroded areas that are equidistant from each other along the axis of rotation.Theoretical analysis and experiments demonstrate that a liquefied layer of granular material oscillates with a radian frequency equal to the angular velocity of the annulus and interacts with the inertial wave it excites.The new phenomenon of libration-induced pattern formation is of practical interest as it can be used to control multiphase flows and mass transfer in rotating containers in a variety of industrial processes.
基金funded by the National Natural Science Foundation of China(12102487)Basic and Applied Basic Research Foundation of Guangdong Province,China(2023A1515012339)+1 种基金Shenzhen Science and Technology Program(ZDSYS20210623091808026)the Discovery Grant(RGPIN-2024-06290)of the Natural Sciences and Engineering Research Council of Canada。
文摘This paper proposed a new libration decoupling analytical speed function(LD-ASF)in lieu of the classic analytical speed function to control the climber's speed along a partial space elevator to improve libration stability in cargo transportation.The LD-ASF is further optimized for payload transportation efficiency by a novel coordinate game theory to balance competing control objectives among payload transport speed,stable end body's libration,and overall control input via model predictive control.The transfer period is divided into several sections to reduce computational burden.The validity and efficacy of the proposed LD-ASF and coordinate game-based model predictive control are demonstrated by computer simulation.Numerical results reveal that the optimized LD-ASF results in higher transportation speed,stable end body's libration,lower thrust fuel consumption,and more flexible optimization space than the classic analytical speed function.
文摘Ⅰ. INTRODUCTIONBesides the theoretical meaning of determining the flee librations itself, we may also infer the excitation and dissipation mechanisms, such as meteorite impact, moonquakes and turbulent core-mantle frictions. Therefore, it will be of great significance to realize the origins, evolutions and structures of the bodies in the solar system.
基金supported by the Russian Science Foundation(Grant No.22-71-00086).
文摘The study of average convection in a rotating cavity subjected to modulated rotation is an interesting area for the development of both fundamental and applied science.This phenomenon finds application in the field of mass transfer and fluid flow control,relevant examples being crystal growth under reduced gravity and fluid mixing in microfluidic devices for cell cultures.In this study,the averaged flow generated by the oscillating motion of a fluid in a planar layer rotating about a horizontal axis is experimentally investigated.The boundaries of the layer are maintained at constant temperatures,while the lateral cylindrical wall is thermally insulated.It is demonstrated that libration results in intense oscillatory fluid motion,which in turn produces a time-averaged flow.For the first time,quantitative measures for the instantaneous velocity field are obtained using the Particle Image Velocimetry technique.It is revealed that the flow has the form of counter-rotating vortices.The vortex circulations sense changes during a libration cycle.An increase in the rotation rate and amplitude of the cavity libration results in an increase in the flow intensity.The heat transfer and time-averaged velocity are examined accordingly as a function of the dimensionless oscillation frequency,and resonant excitation of heat transfer and average oscillation velocity are revealed.The threshold curve for the onset of the averaged convection is identified in the plane of control parameters(dimensionless rotational velocity and pulsation Reynolds number).It is found that an increase in the dimensionless rotational velocity has a stabilizing effect on the onset of convection.
基金supported by the National Key R&D Program of China(2018YFA0703800)the National Natural Science Foundation of China(62173030)the Beijing Natural Science Foundation(4222050).
文摘For mitigating the libration angle fluctuation of the tethered satellite system,this paper discusses how to make the uniform velocity-deceleration separation scheme achieve the best effect.First,a judgment condition is established to determine the tether state by comparing the tether length and the relative distance of the sub-satellite and the parent satellite.Based on the tethered satellite system dynamics equation and Clohessy-Wiltshire equation,dynamic models are given for four cases of tether states.Second,the influence of the uniform velocity-deceleration separation scheme on the libration angle is analyzed by taking the libration angle at the separation ending time and the mean absolute value of the libration angle as index functions.Then,the optimality problem of the uniform velocity-deceleration separation scheme is formulated as an optimization problem with constraints,and an approximate solution algorithm is given by combining the back propagation neural network and Newton-Raphson method of multiple initial values.Finally,the effectiveness of the proposed method is verified by a numerical simulation.
基金National Natural Science Foundation of China (10702003)Innovation Foundation of Beijing University of Aeronautics and Astronautics for Ph.D. Graduates
文摘This article addresses the design of the trajectory transferring from Earth to Halo orbit, and proposes a timing closed-loop strategy of correction maneuver during the transfer in the frame of circular restricted three body problem （CR3BP）. The relation between the Floquet multipliers and the magnitudes of Halo orbit is established, so that the suitable magnitude for the aerospace mission is chosen in terms of the stability of Halo orbit. The stable manifold is investigated from the Poincar6 mapping defined which is different from the previous researches, and six types of single-impulse transfer trajectories are attained from the geometry of the invariant manifolds. Based on one of the trajectories of indirect transfer which are ignored in the most of literatures, the stochastic control theory for imperfect information of the discrete linear stochastic system is applied to design the trajectory correction maneuver. The statistical dispersion analysis is performed by Monte-Carlo simulation,
基金supported by the National Natural Science Foundation of China(Grant No.41590851)the Major State Basic Research Development Program of China(2015CB857101)
文摘The Moon’s physical librations have been extensively studied, and elaborate researches have been developed for the purpose of deriving accurate modes of free librations. Our motivation comes from the Planetary and Lunar Ephemeris DE430 by JPL/NASA, which was created in April 2013,and is reported to be the most accurate lunar ephemeris today using the data from Gravity Recovery and Interior Laboratory（GRAIL）. Therefore, the residuals after fitting the model have reduced owing to improvement in the libration models, and the free librations embedded in the Euler angles have also improved. We use Fourier analysis to extract the approximate frequencies from DE430 and then a quadratic interpolation method is used to determine higher accuracy frequencies. With the frequencies,the linear least-squares fitting method is employed to fit the lunar physical librations to DE430. From this analysis we identified the three modes of free physical librations, and estimated the amplitudes as 1.471′′in longitude, 0.025′′in latitude and 8.19′′× 3.31′′for the wobble, with the respective periods of1056.16, 8806.9 and 27262.99 d. Since the free librations damp with time, they require recent excitation or a continuous stimulating mechanism in order to sustain.
基金was supported by the National Natural Science Foundation of China(No.61021002).
文摘Libration-point missions have been very useful and successful. Due to the unstable natures of most of these orbits, the long-time stationkeeping demands frequent maneuvers and precise orbit determinations. Earth-based tracking will have to undertake much more responsibilities with the increasing number of libration missions. An autonomous navigation system could offer a better way to decrease the need for Earth-based tracking. Nevertheless, when an autonomous navigation system is applied, there are three important factors affecting autonomous navigation accuracy, i.e., the accuracy of initial conditions, the accuracy of measurements, and the accuracy of onboard dynamics for propagation. This paper focuses on analyzing the influence from the third factor and finding an appropriate navigation dynamics, which can satisfy the requirement of estimation accuracy but not cause too much burden for onboard computation. When considering the restricted three-body model and the bicircular restricted four-body model as navigation dynamics, the astrin- gency is not shown during the simulations. Meanwhile, when considering the influences of the Sun＇s direct and indirect perturbations and the eccentricity of the Moon＇s orbit, a new navigation dynamic model with the standard ephemerides is proposed. The simulation shows the feasibility of the proposed model.
基金supports of this study by the National Natural Science Foundation of China (Nos.11773004,61573049,11303001,61571032)the Major Special Project of the National Lunar Exploration of China
文摘Flight schemes for the CHANG＇E-5T1 extended mission are investigated in this paper.In the flight scheme and trajectory design, the remaining propellant of the CHANG＇E-5T1 mission is utilized. The CHANG＇E-5T1 mission is firstly introduced with feasible flight goals derived based on the terminal trajectory and satellite status. The flight schemes are designed to include a lunar return and the libration points in the Sun-Earth/Moon and Earth-Moon systems, with an emphasis on the Earth-Moon triangle libration point thus far unexplored. Secondly, three schemes are proposed for the CHANG＇E-5T1 extended mission with different flight goals. The direct libration point orbit transfer and injection method is adopted to solve the issue in the transfer trajectory design.Furthermore, an innovative concept is proposed to transfer from the Earth-Moon collinear libration point to the triangle point using the Sun-Earth/Moon libration point. Finally, the merits and drawbacks of the three schemes are discussed in terms of flight time, control energy and frequency, flight distance, and goal value. As a result, the scheme including a lunar return and the Earth-Moon L2 libration point is selected for the CHANG＇E-5T1 extended mission. A flight to the Earth-Moon libration point is achieved, replicating the achievement of the ARTEMIS mission.
基金supported by the Discovery Grant (No. RGPIN2018-05991)Discovery Accelerate Supplement Grant (No. RGPAS-2018-522709) of Natural Sciences and Engineering Research Council of CanadaGuangdong Basic and Applied Basic Research Foundation (No. 2019A1515111056)。
文摘This paper studies the libration and stabilization of a parallel partial space elevator system in circular orbits. The system is made up of two paralleled partial space elevators, each of which consists of one main satellite, one end body and a climber moving along the tether between them.The libration characteristics of the elevator are studied through numerical analysis by a new dynamic model, and a novel control strategy is proposed to stabilize the swing of the end body by projecting the climber speeds only. Optimal control method is used to implement the new control strategy in the case where the climbers move in opposite direction. The simulation results validate the effectiveness of the proposed control strategy whose application will neither sacrifice the transport efficiency nor exacerbate libration significantly.
基金the supports of the National Natural Science Foundation of China (Nos.11772009,11402007 and 11672007)the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality
文摘An improved numerical method that can construct Halo/Lissajous orbits in the vicinity of collinear libration points in a full solar system model is investigated. A full solar system gravitational model in the geocentric rotating coordinate system with a clear presentation of the angular velocity relative to the inertial coordinate system is proposed. An alternative way to determine patch points in the multiple shooting method is provided based on a dynamical analysis with Poincare′sections. By employing the new patch points and sequential quadratic programming, Halo orbits for L1, L2, and L3points as well as Lissajous orbits for L1and L2points in the EarthMoon system are generated with the proposed full solar system gravitational model to verify the effectiveness of the proposed method.
文摘The phologravilational restricled three-body problem in which the mass reduclionfactors of two primaries q_1 q_2( -∞, 1] are siudied and an analytic meihod toesli,;iale the number of libralion points ana io calculate lheir hoalion is given in thispaper. The results show lhal in phologravilalional reslricled three-body problem, thenumber of librafion poinis is .from one to seven for different q_1 and q_2. As application,the motion of dust grain like comet tail in the solar syslern is also discussed.
文摘To carry out the deep space exploration tasks near Sun-Earth Libration point L2, the CRTBP dynamic model was built up and the numerical conditional quasi-periodic orbit （Lissajons orbit） was computed near L2. Then, a formation controller was designed with linear matrix inequality to overcome the difficuhy of parameter tuning. To meet the demands of formation accuracy and present thruster＇s capability, a threshold scheme was adopted for formation control. Finally, some numerical simulations and analysis were completed to demonstrate the feasibility of the proposed control strategy.
文摘This paper aims to provide further study on the nonlinear modeling and controller design of formation flying spacecraft in deep space missions. First, in the Sun-Earth system, the nonlinear formation dynamics for the circular restricted three-body problem （CRTBP） and elliptic restricted three-body problem （ERTBP） are presented. Then, with the Floquet mode method, an impulsive controller is developed to keep the Chief on the desired Halo orbit. Finally, a nonlinear adaptive control scheme based on Nonzero set- point LQR and neural network is proposed to achieve high precision formation maneuver and keeping. The simulation results indicate that the proposed nonlinear control strategy is reasonable as it considers not only the orbit keeping of the Chief, but also the formation modeling inaccuracy. Moreover, the nonlinear adaptive control scheme is effective to improve the control accuracy of the formation keeping.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11403013 and 11672126)the Fundamental Research Funds for the Central Universities (Nos. 56XAA14093 and 56YAH12036)the Postdoctoral Foundation of Jiangsu Province (No. 1301029B)
文摘In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semianalytical computation of the center manifolds and the associated canonical transformation are valuable tools for exploring the design space of libration point missions. This paper deals with the refinement of reduction to the center manifold procedure. In order to reduce the amount of calculation needed and avoid repetitive computation of the Poisson bracket, a modified method is presented. By using a polynomial optimization technique, the coordinate transformation is conducted more efficiently. In addition, an alternative way to do the canonical coordinate transformation is discussed, which complements the classical approach. Numerical simulation confirms that more accurate and efficient numerical exploration of the center manifold is made possible by using the refined method.
基金supported by the National Natural Science Foundation of China(10832004)the Fundamental Research Funds for the Central Universities(YWF-10- 02-049)
文摘Spacecrafts in periodic or quasi-periodic orbits near the collinear libration points are proved to be excellent platforms for scientific investigations of various phenomena.Since such periodic or quasi-periodic orbits are exponentially unstable,the station-keeping maneuver is needed. A station-keeping strategy which is found by an analytical method is presented to eradicate the dominant unstable component of the libration point trajectories.The inhibit force transforms the unstable component to a stable component.In this method,it is not necessary to determine a nominal orbit as a reference path.
基金supported by the National Natural Science Foundation of China(10702003)
文摘A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields an unstable linear parameter-varying system with periodic coefficients. Given the variational equations, an innovative control law based on characteristic exponent assignment is introduced for libration point orbit maintenance. A numerical simulation choosing the Richardson＇s third order approximation for a halo orbit as a nominal orbit is conducted, and the results demonstrate the effectiveness of this control law.
文摘To meet the increasing research demand for deep space exploration,especially for the second libration point (L2) conditional periodic orbit (Halo orbit) in the Sun-Earth system,the methods to get analytical Halo orbit and differential-correction Halo orbit were described firstly,and the corresponding orbits accuracy was analyzed.Then,based on the results of third-order and differential-correction Halo orbits,the formation form was studied.Analysis was carried out to discuss the influence of system amplitude,initial phase,and phase difference on the formation form,as well as that of initial orbit values on form accuracy.Finally,some simulation results demonstrate the validity of the proposed methods.
文摘In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The libration points and the corresponding Jacobi constants are obtained with different values of the solar radiation pressure coefficient. The motion and its stability about each point are studied. A family of periodic orbits under the effects of the gravitational forces of the primaries and the solar radiation pressure are obtained depending on the pure numerical method. This purpose is applied to the Sun-Earth-Moon-Space craft system, and the results obtained are in a good agreement with the previous work such as (Kumari and Papadouris, 2013).
文摘This article believes that ＂Chinese Dream＂ has three dimensions： First, ＂Chinese Dream＂ is the inevitable demands of Chinese reconstruction and it is the deepest desire of Chinese nation since the Chinese modern history. Second, the modernism of socialism with Chinese feature is the process of Chinese modernism. Third, the third theoretical dimension, 1 believe, is the ideal of socialism. I would like to take the film ＂Lost＂ and ＂Peking Monk＂ as examples and analyze the specific form of expression. This article is going to indicate in the end that ＂the revolution of aesthetics＂ and the assignments of critics, which can be recognized as the intuitive ability, could merge the historical affair and the human nature, which literature comprise, together and deliver deeper analyses and appraise The mission of critics is not only to distinctly emerge the aesthetic form of the literal works, but also analyze and seize the ＂aesthetic form＂ of them, that is to say, their mission is to find the aesthetic meanings of aesthetic expression from commonage in order to achieve the goal of leading and stimulating people ensuing the consciousness and liberation of culture. That is the most important mission and responsibility of Marxist literal criticism and literal critics. This is a rather tough task and refers to the new understanding and attitude to the relative questions of literature and culture. In the eyes of some self-complacent intellectuals, the responsibility for literature and critics is the ＂aesthetic entertainment＂ and ＂spiritual redemption＂. The significance of Marxist Aesthetics lies in that it upgrades the general ＂literal principle＂ and ＂aesthetic principle＂ in to a level of social development and national deliverance, and also it regards whether the literature having the function of cultural libration as the more pivotal content. The assignment for the critics and litterateurs is to engage and promote the production and promulgate for this significance, the cultural consciousness and liberation.
