Document Details
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Document Type |
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Thesis |
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Document Title |
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Universal Boundary-Value problem of Space dynamics مسألة القيمة الحدية الشاملة لديناميكا الفضاء |
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Subject |
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Boundary value problems. |
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Document Language |
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Arabic |
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Abstract |
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The present thesis aims at studying the universal boundary value problem, which is concerned with the determination of an orbit from two position vectors and the time of flight between them, it is usually called universal Lambert problem. This problem has very important applications in the areas of rendezvous, targeting, guidance, and interplanetary mission.
During space mission all types of the two body motion (elliptic,parabolic,or hyperbolic) appear.For examples the escape from the departure planet and the capture by the target planet involve hyperbolic orbits,while the intermediate stage of the mission commonly depicted as a heliocentric ellipse ,may also be heliocentric parabola or hyperbola. In addition, in some systems, the type of an orbit is occasionally changed by perturbing forces during finite interval of time. Thus far we have been obliged to use different functional representations for motion depending upon the energy state (elliptic, parabolic, or hyperbolic) and a simulation code must then contain branching to handle a switch from one state to another .In cases where this switching is not smooth, branching can occur many times during a single integration time-step causing some numerical “chatter”. Consequently,universal formulations are desperately needed so that ,orbit predictions will be free of the troubles ,since a single functional representation suffices to describe all possible states.
For these resons, and the importance of the boundary value problem ,as mentioned brifly in the above ,the present thesis is devoted for the study of the boundary value problem in its universal form.
The present thesis comprise two parts : in the first part the properties of the orbital boundary value problem are presented including terminal velocity vectors with different coordinates and the minimum energy orbit with it's various orbital elements. The fundamental ellipse is discussed, together with the various forms of its parameters.All of these properties are proved mathematically and illustrated geometrically.
The second part of the thesis is devoted to the solution of Lambert problem for different conic sections .In this respect we considered :
• "Gauss Method": for elliptic orbits, the equations of the method together with the its computational algorithm are presented .
• "The iterative method" : for elliptic orbits ,by which the values of semi major axis and each Lagrange coefficients "f" and "g", are computed so as to determine the initial velocity .
Also some methods for solving universal Lambert problem are discussed, including:
• "Linear terminal velocity constrain": for which, the basic equations, computational algorithms and some numerical applications are given.
• "Computational algorithms" to solve universal Lambert problem, and, the basic equations, some numerical applications are given.
• "Battin's method": for which the basic equations and computational algorithms are given in full details .In addition, we implement the method to compute the geometric characteristics of the boundary value problem (demonstrated in the first part). Finally we made use of these computed geometric characteristics as criteria for accuracy checks of the calculations. The algorithms is applied to 14 orbits of different eccentricity ,the numerical results are extremely accurate |
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Supervisor |
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Mohammed Adel Sharaf |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1434 AH
2013 AD |
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Number Of Pages |
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116 |
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Co-Supervisor |
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Hasan Asiri |
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Added Date |
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Monday, September 30, 2013 |
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Researchers
| ريم مقبول القثامي | Al-Gethamie, Reem Magboul | Investigator | Master | |
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