<jats:p>In the present article, we have investigated a new family of nonsingular solutions of static relativistic compact sphere which incorporates the characteristics of anisotropic fluid and electromagnetic field in the context of minimally coupled <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>f</mi> <mfenced open="(" close=")" separators="|"> <mrow> <mi>R</mi> </mrow> </mfenced> </math> </jats:inline-formula> theory of gravity. The strange matter <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <mtext>MIT</mtext> </math> </jats:inline-formula> bag model equation of state (EoS) has been considered along with the usual forms of the Karori–Barua <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <mfenced open="(" close=")" separators="|"> <mrow> <mtext>KB</mtext> </mrow> </mfenced> </math> </jats:inline-formula> metric potentials. For this purpose, we derived the Einstein–Maxwell field equations in the assistance of strange matter EoS and <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"> <mtext>KB</mtext> </math> </jats:inline-formula> type ansatz by employing the two viable and cosmologically well-consistent models of <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M6"> <mi>f</mi> <mfenced open="(" close=")" separators="|"> <mrow> <mi>R</mi> </mrow> </mfenced> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mi>γ</mi> <msup> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </math> </jats:inline-formula> and <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M7"> <mi>f</mi> <mfenced open="(" close=")" separators="|"> <mrow> <mi>R</mi> </mrow>
{"title":"Model of Charged Anisotropic Strange Stars in Minimally Coupled \u0000 f\u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 Gravity","authors":"H. Nazar, G. Abbas","doi":"10.1155/2021/6698208","DOIUrl":"https://doi.org/10.1155/2021/6698208","url":null,"abstract":"<jats:p>In the present article, we have investigated a new family of nonsingular solutions of static relativistic compact sphere which incorporates the characteristics of anisotropic fluid and electromagnetic field in the context of minimally coupled <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>f</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> theory of gravity. The strange matter <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mtext>MIT</mtext>\u0000 </math>\u0000 </jats:inline-formula> bag model equation of state (EoS) has been considered along with the usual forms of the Karori–Barua <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mtext>KB</mtext>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> metric potentials. For this purpose, we derived the Einstein–Maxwell field equations in the assistance of strange matter EoS and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mtext>KB</mtext>\u0000 </math>\u0000 </jats:inline-formula> type ansatz by employing the two viable and cosmologically well-consistent models of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mi>f</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>=</mo>\u0000 <mi>R</mi>\u0000 <mo>+</mo>\u0000 <mi>γ</mi>\u0000 <msup>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\u0000 <mi>f</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46672764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present paper deals with the study of the motion’s properties of the infinitesimal variable mass body moving in the same orbital plan as two massive bodies (considered as primaries). It is assumed that the massive bodies have radiating effects, have oblate shapes, and are moving in circular orbits around their common center of mass. Using the procedures established by Singh and Abouelmagd, we determined the equations of motion of the infinitesimal body for which we assumed that under the effects of radiation and oblateness of the primaries, its mass varies following Jean’s law. We evaluated analytically and numerically the locations of equilibrium points and examined the stability of these equilibrium points. Finally, we found that all the points are unstable.
{"title":"Motion of the Infinitesimal Variable Mass in the Generalized Circular Restricted Three-Body Problem under the Effect of Asteroids Belt","authors":"F. Bouaziz-Kellil","doi":"10.1155/2020/6684728","DOIUrl":"https://doi.org/10.1155/2020/6684728","url":null,"abstract":"The present paper deals with the study of the motion’s properties of the infinitesimal variable mass body moving in the same orbital plan as two massive bodies (considered as primaries). It is assumed that the massive bodies have radiating effects, have oblate shapes, and are moving in circular orbits around their common center of mass. Using the procedures established by Singh and Abouelmagd, we determined the equations of motion of the infinitesimal body for which we assumed that under the effects of radiation and oblateness of the primaries, its mass varies following Jean’s law. We evaluated analytically and numerically the locations of equilibrium points and examined the stability of these equilibrium points. Finally, we found that all the points are unstable.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42526440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Elbaz I. Abouelmagd, Mitali J. Doshi, Niraj M. Pathak
In the framework of formation satellites, the periodic orbits of deputy satellite are analyzed when the chief satellite is moving in an elliptical orbit. This analysis is developed on 1- to 10-loop periodic orbits of the deputy satellite. These orbits along with their associated loops are discussed under some specific initial position sets. The effects of different initial velocities, initial true anomalies, and eccentricities on the initial position and orbital period of periodic orbits of deputy satellite are investigated.
{"title":"Evolution of Periodic Orbits within the Frame of Formation Satellites","authors":"Elbaz I. Abouelmagd, Mitali J. Doshi, Niraj M. Pathak","doi":"10.1155/2020/1348319","DOIUrl":"https://doi.org/10.1155/2020/1348319","url":null,"abstract":"In the framework of formation satellites, the periodic orbits of deputy satellite are analyzed when the chief satellite is moving in an elliptical orbit. This analysis is developed on 1- to 10-loop periodic orbits of the deputy satellite. These orbits along with their associated loops are discussed under some specific initial position sets. The effects of different initial velocities, initial true anomalies, and eccentricities on the initial position and orbital period of periodic orbits of deputy satellite are investigated.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46318417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we investigate the problem of constructing new integrable problems in the dynamics of the rigid body rotating about its fixed point as results of the effect of a combination of potential and gyroscopic forces possessing a common symmetry axis. We introduce two new integrable problems in a rigid body dynamics that generalize some integrable problems in this field, known by names of Chaplygin and Yehia–Elmandouh.
{"title":"Quartic Integral in Rigid Body-Gyrostat Dynamics","authors":"C. Mnasri, A. Elmandouh","doi":"10.1155/2020/6651277","DOIUrl":"https://doi.org/10.1155/2020/6651277","url":null,"abstract":"In this work, we investigate the problem of constructing new integrable problems in the dynamics of the rigid body rotating about its fixed point as results of the effect of a combination of potential and gyroscopic forces possessing a common symmetry axis. We introduce two new integrable problems in a rigid body dynamics that generalize some integrable problems in this field, known by names of Chaplygin and Yehia–Elmandouh.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":"2020 1","pages":"1-16"},"PeriodicalIF":1.4,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44411882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the problem of the motion of a rigid body about a fixed point under the action of a Newtonian force field is studied when the natural frequency . This case of singularity appears in the previous works and deals with different bodies which are classified according to the moments of inertia. Using the large parameter method, the periodic solutions for the equations of motion of this problem are obtained in terms of a large parameter, which will be defined later. The geometric interpretation of the considered motion will be given in terms of Euler’s angles. The numerical solutions for the system of equations of motion are obtained by one of the well-known numerical methods. The comparison between the obtained numerical solutions and analytical ones is carried out to show the errors between them and to prove the accuracy of both used techniques. In the end, we obtain the case of the regular precession type as a special case. The stability of the motion is considered by the phase diagram procedures.
{"title":"New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency","authors":"A. I. Ismail","doi":"10.1155/2020/6629183","DOIUrl":"https://doi.org/10.1155/2020/6629183","url":null,"abstract":"In this paper, the problem of the motion of a rigid body about a fixed point under the action of a Newtonian force field is studied when the natural frequency . This case of singularity appears in the previous works and deals with different bodies which are classified according to the moments of inertia. Using the large parameter method, the periodic solutions for the equations of motion of this problem are obtained in terms of a large parameter, which will be defined later. The geometric interpretation of the considered motion will be given in terms of Euler’s angles. The numerical solutions for the system of equations of motion are obtained by one of the well-known numerical methods. The comparison between the obtained numerical solutions and analytical ones is carried out to show the errors between them and to prove the accuracy of both used techniques. In the end, we obtain the case of the regular precession type as a special case. The stability of the motion is considered by the phase diagram procedures.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":"1-12"},"PeriodicalIF":1.4,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47629560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A systematic examination of the basic theory of general relativity is made, the meaning of coordinates again is emphasized, the confusion caused by unclear meaning of coordinates in the past is corrected, and the expression of the theory is made more accurate. Firstly, the equation of Einstein’s gravitational field is solved in the usual coordinate system, the existence of light speed invariant solution in the spherically symmetric gravitational field is proved, and in the same time, the solution is determined. It turns out that black holes are not an inevitable prediction of general relativity. +e more exact formulas for calculating the curvature of light on the surface of the Sun and the precession angle of the orbit of Mercury are given, and the convergence of general relativistic gravity and special relativistic mechanics under the weak field approximation is realized. Finally, it is shown that the coupling coefficient of the gravitational field equation is not unique. Modifying this coefficient is an ideal project to eliminate the singularities of general relativity on the condition keeping the field equation concise and elegant, and moreover, it reveals that dark matter and dark energy are the negative energy field in the matter, the expansion of the universe is the appearance of the gradual formation of galaxies in accordance with fractal rules, not only the space between galaxies is expanding but also the galaxies themselves are also expanding, new matter is continuously generated in the celestial bodies, for the first time, the unity of fractal geometry and cosmic dynamics of general relativity is realized, and the formation and evolution of galaxies are brought into the fractal generation mode. +is is a living and vivacious universe in which all aspects are gradually strengthening, in sharp contrast to the dying universe under the current cosmological framework.
{"title":"Light Speed Invariant Solution and Its Enlightenment of Field Equation of General Relativity","authors":"J. Yang","doi":"10.1155/2020/3930947","DOIUrl":"https://doi.org/10.1155/2020/3930947","url":null,"abstract":"A systematic examination of the basic theory of general relativity is made, the meaning of coordinates again is emphasized, the confusion caused by unclear meaning of coordinates in the past is corrected, and the expression of the theory is made more accurate. Firstly, the equation of Einstein’s gravitational field is solved in the usual coordinate system, the existence of light speed invariant solution in the spherically symmetric gravitational field is proved, and in the same time, the solution is determined. It turns out that black holes are not an inevitable prediction of general relativity. +e more exact formulas for calculating the curvature of light on the surface of the Sun and the precession angle of the orbit of Mercury are given, and the convergence of general relativistic gravity and special relativistic mechanics under the weak field approximation is realized. Finally, it is shown that the coupling coefficient of the gravitational field equation is not unique. Modifying this coefficient is an ideal project to eliminate the singularities of general relativity on the condition keeping the field equation concise and elegant, and moreover, it reveals that dark matter and dark energy are the negative energy field in the matter, the expansion of the universe is the appearance of the gradual formation of galaxies in accordance with fractal rules, not only the space between galaxies is expanding but also the galaxies themselves are also expanding, new matter is continuously generated in the celestial bodies, for the first time, the unity of fractal geometry and cosmic dynamics of general relativity is realized, and the formation and evolution of galaxies are brought into the fractal generation mode. +is is a living and vivacious universe in which all aspects are gradually strengthening, in sharp contrast to the dying universe under the current cosmological framework.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":"2020 1","pages":"1-12"},"PeriodicalIF":1.4,"publicationDate":"2020-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43766946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-23DOI: 10.22541/au.160616166.67887623/v1
E. Abdel-salam, M. Nouh, Y. A. Azzam, M. Jazmati
The helium burning phase represents the second stage that the star used to consume nuclear fuel in its interior. In this stage, the three elements, carbon, oxygen, and neon, are synthesized. The present paper is twofold: firstly, it develops an analytical solution to the system of the conformable fractional differential equations of the helium burning network, where we used, for this purpose, the series expansion method and obtained recurrence relations for the product abundances, that is, helium, carbon, oxygen, and neon. Using four different initial abundances, we calculated 44 gas models covering the range of the fractional parameterα=0.5−1with stepΔα=0.05. We found that the effects of the fractional parameter on the product abundances are small which coincides with the results obtained by a previous study. Secondly, we introduced the mathematical model of the neural network (NN) and developed a neural network algorithm to simulate the helium burning network using a feed-forward process. A comparison between the NN and the analytical models revealed very good agreement for all gas models. We found that NN could be considered as a powerful tool to solve and model nuclear burning networks and could be applied to the other nuclear stellar burning networks.
{"title":"Conformable Fractional Models of the Stellar Helium Burning via Artificial Neural Networks","authors":"E. Abdel-salam, M. Nouh, Y. A. Azzam, M. Jazmati","doi":"10.22541/au.160616166.67887623/v1","DOIUrl":"https://doi.org/10.22541/au.160616166.67887623/v1","url":null,"abstract":"The helium burning phase represents the second stage that the star used to consume nuclear fuel in its interior. In this stage, the three elements, carbon, oxygen, and neon, are synthesized. The present paper is twofold: firstly, it develops an analytical solution to the system of the conformable fractional differential equations of the helium burning network, where we used, for this purpose, the series expansion method and obtained recurrence relations for the product abundances, that is, helium, carbon, oxygen, and neon. Using four different initial abundances, we calculated 44 gas models covering the range of the fractional parameterα=0.5−1with stepΔα=0.05. We found that the effects of the fractional parameter on the product abundances are small which coincides with the results obtained by a previous study. Secondly, we introduced the mathematical model of the neural network (NN) and developed a neural network algorithm to simulate the helium burning network using a feed-forward process. A comparison between the NN and the analytical models revealed very good agreement for all gas models. We found that NN could be considered as a powerful tool to solve and model nuclear burning networks and could be applied to the other nuclear stellar burning networks.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2020-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49389905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this recent study, we shall investigate the wormhole models with a Hu–Sawicki model in the framework of gravity. Spherically static symmetric space-time is considered to construct wormhole models with the anisotropic fluid distribution. The traceless matter is discussed by imposing a particular equation of state. To address the important conditions of the shape function of the wormhole geometry, we have used the particular values of the involved parameters. Furthermore, different energy conditions are discussed to check the nature of matter against two specific models. The null energy condition is observed to be violated for both of the models. It is mentioned that our inquired results are acceptable.
{"title":"Wormhole Models and Energy Conditions in \u0000 f\u0000 \u0000 \u0000 ℛ\u0000 \u0000 \u0000 Gravity with the Hu–Sawicki Model","authors":"Ouziala Ikram, G. Mustafa","doi":"10.1155/2020/8813611","DOIUrl":"https://doi.org/10.1155/2020/8813611","url":null,"abstract":"In this recent study, we shall investigate the wormhole models with a Hu–Sawicki model in the framework of gravity. Spherically static symmetric space-time is considered to construct wormhole models with the anisotropic fluid distribution. The traceless matter is discussed by imposing a particular equation of state. To address the important conditions of the shape function of the wormhole geometry, we have used the particular values of the involved parameters. Furthermore, different energy conditions are discussed to check the nature of matter against two specific models. The null energy condition is observed to be violated for both of the models. It is mentioned that our inquired results are acceptable.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":"2020 1","pages":"1-12"},"PeriodicalIF":1.4,"publicationDate":"2020-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64753502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present paper, we have introduced a new model of gravastar with an isotropic matter distribution in Rastall gravity by the Mazur–Mottola (2004) mechanism. Mazur–Mottola approach is about the construction of gravastar which is predicted as an alternative to black hole. By following this convention, we define gravastar in the form of three phases. The first one is an interior phase which has negative density; the second part consists of thin shell comprising ultrarelativistic stiff fluid for which we have discussed the length, energy, and entropy. By the graphical analysis of entropy, we have shown that our proposed thin shell gravastar model is potentially stable. The third phase of gravastar is defined by the exterior Schwarzschild geometry. For the interior of gravastar, we have found the analytical solutions free from any singularity and the event horizon in the framework of Rastall gravity.
{"title":"Isotropic Gravastar Model in Rastall Gravity","authors":"G. Abbas, K. Majeed","doi":"10.1155/2020/8861168","DOIUrl":"https://doi.org/10.1155/2020/8861168","url":null,"abstract":"In the present paper, we have introduced a new model of gravastar with an isotropic matter distribution in Rastall gravity by the Mazur–Mottola (2004) mechanism. Mazur–Mottola approach is about the construction of gravastar which is predicted as an alternative to black hole. By following this convention, we define gravastar in the form of three phases. The first one is an interior phase which has negative density; the second part consists of thin shell comprising ultrarelativistic stiff fluid for which we have discussed the length, energy, and entropy. By the graphical analysis of entropy, we have shown that our proposed thin shell gravastar model is potentially stable. The third phase of gravastar is defined by the exterior Schwarzschild geometry. For the interior of gravastar, we have found the analytical solutions free from any singularity and the event horizon in the framework of Rastall gravity.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":"1-10"},"PeriodicalIF":1.4,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/8861168","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49200638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We illustrate the chaotic nature of the circular restricted three-body problem from the perspective of the bifurcation diagram with respect to the mass ratio parameter. Moreover, it is shown that when the frequency ratio in different directions of the classical problem is irrational, it has the quasiperiodic characteristics. In addition, a three-dimensional approximate solution to this problem under two time scales is proposed by using the multiple time scales method.
{"title":"Approximate Analytical Three-Dimensional Multiple Time Scales Solution to a Circular Restricted Three-Body Problem","authors":"F. Gao, Yongqing Wang","doi":"10.1155/2020/8868137","DOIUrl":"https://doi.org/10.1155/2020/8868137","url":null,"abstract":"We illustrate the chaotic nature of the circular restricted three-body problem from the perspective of the bifurcation diagram with respect to the mass ratio parameter. Moreover, it is shown that when the frequency ratio in different directions of the classical problem is irrational, it has the quasiperiodic characteristics. In addition, a three-dimensional approximate solution to this problem under two time scales is proposed by using the multiple time scales method.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":"1-10"},"PeriodicalIF":1.4,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47176788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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