The present manuscript examines the circular restricted gravitational three-body problem (CRGTBP) by the introduction of a new approach through the power series method. In addition, certain computational algorithms wi...The present manuscript examines the circular restricted gravitational three-body problem (CRGTBP) by the introduction of a new approach through the power series method. In addition, certain computational algorithms with the aid of Mathematica software are specifically designed for the problem. The algorithms or rather mathematical modules are established to determine the velocity and position of the third body’s motion. In fact, the modules led to accurate results and thus proved the new approach to be efficient.展开更多
By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution ...By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution is equal to the result of separation of variables. As a result, the non-linear characteristic equations resulting from the method of separation of variables are transformed into polynomial equations that can provide a foundation for approximate computation and asymptotic analysis.展开更多
Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then trans...Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.展开更多
In this paper, a new approach called Power Series Approximation Method (PSAM) is developed for the numerical solution of a generalized linear and non-linear higher order Boundary Value Problems (BVPs). The proposed me...In this paper, a new approach called Power Series Approximation Method (PSAM) is developed for the numerical solution of a generalized linear and non-linear higher order Boundary Value Problems (BVPs). The proposed method is efficient and effective on the experimentation on some selected thirteen-order, twelve-order and ten-order boundary value problems as compared with the analytic solutions and other existing methods such as the Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) available in the literature. A convergence analysis of PSAM is also provided.展开更多
This review article aims to give a comprehensive review of periodic orbits in the circular restricted three-body problem(CRTBP),which is a standard ideal model for the Earth-Moon system and is closest to the practical...This review article aims to give a comprehensive review of periodic orbits in the circular restricted three-body problem(CRTBP),which is a standard ideal model for the Earth-Moon system and is closest to the practical mechanical model.It focuses the attention on periodic orbits in the Earth-Moon system.This work is primarily motivated by a series of missions and plans that take advantages of the three-body periodic orbits near the libration points or around two gravitational celestial bodies.Firstly,simple periodic orbits and their classification that is usually considered to be early work before 1970 are summarized,and periodic orbits around Lagrange points,either planar or three-dimensional,are intensively studied during past decades.Subsequently,stability index of a periodic orbit and bifurcation analysis are presented,which demonstrate a guideline to find more periodic orbits inspired by bifurcation signals.Then,the practical techniques for computing a wide range of periodic orbits and associated quasi-periodic orbits,as well as constructing database of periodic orbits by numerical searching techniques are also presented.For those unstable periodic orbits,the station keeping maneuvers are reviewed.Finally,the applications of periodic orbits are presented,including those in practical missions,under consideration,and still in conceptual design stage.This review article has the function of bridging between engineers and researchers,so as to make it more convenient and faster for engineers to understand the complex restricted three-body problem(RTBP).At the same time,it can also provide some technical thinking for general researchers.展开更多
The Three-Body Problem, written by Liu Cixin, won the 2015 Hugo Award for Best Novel, with over 200,000 copies in English already sold. This gure is hundreds of times the average sales volume of Chinese novels in the ...The Three-Body Problem, written by Liu Cixin, won the 2015 Hugo Award for Best Novel, with over 200,000 copies in English already sold. This gure is hundreds of times the average sales volume of Chinese novels in the USA. Through qualitative and quantitative analyses of overseas readers' comments on The Three-Body Problem posted on the online platforms of Goodreads and Amazon, this paper concludes that the novel's success overseas lies in its catering to the concerns of overseas readers. The ThreeBody Problem is popular among overseas readership thanks to its re ection on the ultimate existence of mankind, science ction vision & imagination, literary familiarity & identi cation, ideological di erence-triggered cultural curiosity, and a good translation. This paper attempts to interpret Liu Cixin's work on the map of world literature from the perspective of overseas readers' preferences to provide references for contemporary Chinese science ction creation and overseas reception.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
In this article we study the estimation method of nonparametric regression measurement error model based on a validation data. The estimation procedures are based on orthogonal series estimation and truncated series a...In this article we study the estimation method of nonparametric regression measurement error model based on a validation data. The estimation procedures are based on orthogonal series estimation and truncated series approximation methods without specifying any structure equation and the distribution assumption. The convergence rates of the proposed estimator are derived. By example and through simulation, the method is robust against the misspecification of a measurement error model.展开更多
The Feshbach-Rubinow approximation and its improved versions have been appfied to the H＋ ion system. The ground-state energies are caJculated with these different methods. The best ground-state energy obtained is onl...The Feshbach-Rubinow approximation and its improved versions have been appfied to the H＋ ion system. The ground-state energies are caJculated with these different methods. The best ground-state energy obtained is only 2% higher than the experimental result. Given the simplicity of the method, this accuracy is quite remarkable. It is shown that the screening effect plays a less significant role and the effective potential between the two protons is probably of most importance in this problem.展开更多
We found another critical mass ratio value -↑μ between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has ...We found another critical mass ratio value -↑μ between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has not been pointed out before. We used numerical computations to show how the long period family evolves around this critical value. The case is similar to that of the critical values between μ2 and μ4, with slight difference in evolution details.展开更多
The Method Of Lines (MOL) and Scheifele’s G-functions in the design of algorithms adapted for the numeric integration of parabolic Partial Differential Equations (PDE) in one space dimension are applied. The semi-dis...The Method Of Lines (MOL) and Scheifele’s G-functions in the design of algorithms adapted for the numeric integration of parabolic Partial Differential Equations (PDE) in one space dimension are applied. The semi-discrete system of ordinary differential equations in the time direction, obtained by applying the MOL to PDE, is solved with the use of a method of Adapted Series, based on Scheifele’s G-functions. This method integrates exactly unperturbed linear systems of ordinary differential equations, with only one G-function. An implementation of this algorithm is used to approximate the solution of two test problems proposed by various authors. The results obtained by the Dufort-Frankel, Crank-Nicholson and the methods of Adapted Series versus the analytical solution, show the results of mistakes made.展开更多
In this article we analyze the motion of a test particle of a planar, circular, restricted three-body problem in resonance, using the Kustaanheimo-Stiefel formalism. We show that a good qualitative description of the ...In this article we analyze the motion of a test particle of a planar, circular, restricted three-body problem in resonance, using the Kustaanheimo-Stiefel formalism. We show that a good qualitative description of the motion can be reduced to three simple equations for semi-major axis, eccentricity and resonance angle. Studying these equations reveals the onset of chaos, and sheds a new light on its weak nature. The 7:4 resonance is used as an example.展开更多
The dynamics of satellites formation is of great interest for the space mission. This work discusses a more efficient model of the relative motion dynamics of satellites formation. The model is based on employing the ...The dynamics of satellites formation is of great interest for the space mission. This work discusses a more efficient model of the relative motion dynamics of satellites formation. The model is based on employing the concepts restricted three-body problem (R3BP) and for more accuracy, it considers the effects of both oblateness and radiation pressure on deputy relative motion w.r.t the chief satellite. A model of deputy relative motion w.r.t the chief satellite is derived in the local-vertical local-horizontal system and simplified assuming the concept of the circular restricted three-body problem (CR3BP). The deputy equations of motion were rewritten in the form of recurrence relations and solved numerically using the Lie series approach. Assuming that the formation is revolving around the Moon in the Earth-Moon system, the effects of both oblateness and radiation pressure on the deputy satellite orbit were assessed through a particular example of satellites formation. A comparison between the perturbed and unperturbed R3BP shows a significant difference in the deputy relative position that has to be considered for the formation dynamics.展开更多
The greatest charm of science fiction is not the artistic imagination, but the scientific imagination.Liu Cixin＇s the Three-body Problem as a Chinese science fiction novel, reflected Chinese writer how to think scien...The greatest charm of science fiction is not the artistic imagination, but the scientific imagination.Liu Cixin＇s the Three-body Problem as a Chinese science fiction novel, reflected Chinese writer how to think science and technology and its possible future of mankind＇s imagination. This novel contained ＂Deconstruction＂ Utopia, ＂Transcendence＂ dystopia and ＂Composited＂ Heterotopias, Which fully demonstrated singularity politics＇s great ideological tension between post modernity thinking of in this or that and typical Chinese style doctrine and dialectics.展开更多
We study of halo orbits in the circular restricted three-body problem (CRTBP) with both the primaries as sources of radiation. The positioning of the triangular equilibrium points is discussed in a rotating coordinate...We study of halo orbits in the circular restricted three-body problem (CRTBP) with both the primaries as sources of radiation. The positioning of the triangular equilibrium points is discussed in a rotating coordinate system.展开更多
This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium point...This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.展开更多
In the present work, the collinear equilibrium points of the restricted three-body problem are studied under the effect of oblateness of the bigger primary using an analytical and numerical approach. The periodic orbi...In the present work, the collinear equilibrium points of the restricted three-body problem are studied under the effect of oblateness of the bigger primary using an analytical and numerical approach. The periodic orbits around these points are investigated for the Earth-Moon system. The Lissajous orbits and the phase spaces are obtained under the effect of oblateness.展开更多
文摘The present manuscript examines the circular restricted gravitational three-body problem (CRGTBP) by the introduction of a new approach through the power series method. In addition, certain computational algorithms with the aid of Mathematica software are specifically designed for the problem. The algorithms or rather mathematical modules are established to determine the velocity and position of the third body’s motion. In fact, the modules led to accurate results and thus proved the new approach to be efficient.
基金Supported by the National Natural Science Foundation of Chinathe Doctoral Training of the State Education Commission of China
文摘By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution is equal to the result of separation of variables. As a result, the non-linear characteristic equations resulting from the method of separation of variables are transformed into polynomial equations that can provide a foundation for approximate computation and asymptotic analysis.
文摘Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.
文摘In this paper, a new approach called Power Series Approximation Method (PSAM) is developed for the numerical solution of a generalized linear and non-linear higher order Boundary Value Problems (BVPs). The proposed method is efficient and effective on the experimentation on some selected thirteen-order, twelve-order and ten-order boundary value problems as compared with the analytic solutions and other existing methods such as the Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) available in the literature. A convergence analysis of PSAM is also provided.
文摘This review article aims to give a comprehensive review of periodic orbits in the circular restricted three-body problem(CRTBP),which is a standard ideal model for the Earth-Moon system and is closest to the practical mechanical model.It focuses the attention on periodic orbits in the Earth-Moon system.This work is primarily motivated by a series of missions and plans that take advantages of the three-body periodic orbits near the libration points or around two gravitational celestial bodies.Firstly,simple periodic orbits and their classification that is usually considered to be early work before 1970 are summarized,and periodic orbits around Lagrange points,either planar or three-dimensional,are intensively studied during past decades.Subsequently,stability index of a periodic orbit and bifurcation analysis are presented,which demonstrate a guideline to find more periodic orbits inspired by bifurcation signals.Then,the practical techniques for computing a wide range of periodic orbits and associated quasi-periodic orbits,as well as constructing database of periodic orbits by numerical searching techniques are also presented.For those unstable periodic orbits,the station keeping maneuvers are reviewed.Finally,the applications of periodic orbits are presented,including those in practical missions,under consideration,and still in conceptual design stage.This review article has the function of bridging between engineers and researchers,so as to make it more convenient and faster for engineers to understand the complex restricted three-body problem(RTBP).At the same time,it can also provide some technical thinking for general researchers.
文摘The Three-Body Problem, written by Liu Cixin, won the 2015 Hugo Award for Best Novel, with over 200,000 copies in English already sold. This gure is hundreds of times the average sales volume of Chinese novels in the USA. Through qualitative and quantitative analyses of overseas readers' comments on The Three-Body Problem posted on the online platforms of Goodreads and Amazon, this paper concludes that the novel's success overseas lies in its catering to the concerns of overseas readers. The ThreeBody Problem is popular among overseas readership thanks to its re ection on the ultimate existence of mankind, science ction vision & imagination, literary familiarity & identi cation, ideological di erence-triggered cultural curiosity, and a good translation. This paper attempts to interpret Liu Cixin's work on the map of world literature from the perspective of overseas readers' preferences to provide references for contemporary Chinese science ction creation and overseas reception.
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.
文摘In this article we study the estimation method of nonparametric regression measurement error model based on a validation data. The estimation procedures are based on orthogonal series estimation and truncated series approximation methods without specifying any structure equation and the distribution assumption. The convergence rates of the proposed estimator are derived. By example and through simulation, the method is robust against the misspecification of a measurement error model.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10735010,10975072,and 11035001by the 973 National Major State Basic Research and Development of China under Grant Nos. 2007CB815004 and 2010CB327803
文摘The Feshbach-Rubinow approximation and its improved versions have been appfied to the H＋ ion system. The ground-state energies are caJculated with these different methods. The best ground-state energy obtained is only 2% higher than the experimental result. Given the simplicity of the method, this accuracy is quite remarkable. It is shown that the screening effect plays a less significant role and the effective potential between the two protons is probably of most importance in this problem.
基金Supported by the National Natural Science Foundation of China
文摘We found another critical mass ratio value -↑μ between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has not been pointed out before. We used numerical computations to show how the long period family evolves around this critical value. The case is similar to that of the critical values between μ2 and μ4, with slight difference in evolution details.
文摘The Method Of Lines (MOL) and Scheifele’s G-functions in the design of algorithms adapted for the numeric integration of parabolic Partial Differential Equations (PDE) in one space dimension are applied. The semi-discrete system of ordinary differential equations in the time direction, obtained by applying the MOL to PDE, is solved with the use of a method of Adapted Series, based on Scheifele’s G-functions. This method integrates exactly unperturbed linear systems of ordinary differential equations, with only one G-function. An implementation of this algorithm is used to approximate the solution of two test problems proposed by various authors. The results obtained by the Dufort-Frankel, Crank-Nicholson and the methods of Adapted Series versus the analytical solution, show the results of mistakes made.
文摘In this article we analyze the motion of a test particle of a planar, circular, restricted three-body problem in resonance, using the Kustaanheimo-Stiefel formalism. We show that a good qualitative description of the motion can be reduced to three simple equations for semi-major axis, eccentricity and resonance angle. Studying these equations reveals the onset of chaos, and sheds a new light on its weak nature. The 7:4 resonance is used as an example.
文摘The dynamics of satellites formation is of great interest for the space mission. This work discusses a more efficient model of the relative motion dynamics of satellites formation. The model is based on employing the concepts restricted three-body problem (R3BP) and for more accuracy, it considers the effects of both oblateness and radiation pressure on deputy relative motion w.r.t the chief satellite. A model of deputy relative motion w.r.t the chief satellite is derived in the local-vertical local-horizontal system and simplified assuming the concept of the circular restricted three-body problem (CR3BP). The deputy equations of motion were rewritten in the form of recurrence relations and solved numerically using the Lie series approach. Assuming that the formation is revolving around the Moon in the Earth-Moon system, the effects of both oblateness and radiation pressure on the deputy satellite orbit were assessed through a particular example of satellites formation. A comparison between the perturbed and unperturbed R3BP shows a significant difference in the deputy relative position that has to be considered for the formation dynamics.
文摘The greatest charm of science fiction is not the artistic imagination, but the scientific imagination.Liu Cixin＇s the Three-body Problem as a Chinese science fiction novel, reflected Chinese writer how to think science and technology and its possible future of mankind＇s imagination. This novel contained ＂Deconstruction＂ Utopia, ＂Transcendence＂ dystopia and ＂Composited＂ Heterotopias, Which fully demonstrated singularity politics＇s great ideological tension between post modernity thinking of in this or that and typical Chinese style doctrine and dialectics.
文摘We study of halo orbits in the circular restricted three-body problem (CRTBP) with both the primaries as sources of radiation. The positioning of the triangular equilibrium points is discussed in a rotating coordinate system.
文摘This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.
文摘In the present work, the collinear equilibrium points of the restricted three-body problem are studied under the effect of oblateness of the bigger primary using an analytical and numerical approach. The periodic orbits around these points are investigated for the Earth-Moon system. The Lissajous orbits and the phase spaces are obtained under the effect of oblateness.
