Document Details
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Document Type |
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Thesis |
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Document Title |
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Analytical and Computational Treatment of the Restricted Three-Body Problem and its معالجة تحليلية وحسابية لمسألة الأجسام الثلاثة المقيدة وتطبيقاتها |
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Subject |
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Astronomy department |
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Document Language |
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Arabic |
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Abstract |
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The present thesis explores the analytical and numerical aspects of the restricted three body problem that are of relevance to the orbital dynamics for artificial satellites as well as for planetary bodies.
For the analytical aspects, which are the subjects of the first two chapters .In the Chapter I, we developed Lagrange's equilateral triangle solution, straight line solutions and conic section solution on the bases of the kinematics in rotating coordinates. Also, symbolic analytical solutions to Lagrange's quintic equation was established using series reversion of power series. These, symbolic solutions are applied to Earth-Moon-Spacecraft system. In Chapter II, four set of the equations of motion are derived for the planar restricted circular three-body problem. Also, Lagrangian and Hamiltonian functions are listed for the restricted three body problem. Computation algorithm for the location of the Lagrangian points is also developed on the bases of , symbolic solutions of Lagrange's quintic equation. Stability analysis of the five Lagrangian points is studied in detailed using matrix eigenvalue problem .Three developed, these applications are applications of the Jacobi's integral were also:
♦Tisserand's criterion for the identification of comets.
♦Rectilinear oscillation of an infinitesimal mass.
♦ Surfaces of zero relative velocity.
Moreover, the reduction of the differential equations of motion to the second orders is also developed. Finally, power series solution of the planer restricted three –body problem is established, and some symbolic expressions for the power series coefficients are also given.
For the numerical applications aspects which are the subjects of Chapter IV. In this chapter, we discussed first three basic aspects concerning the applications of the planar restricted circular three-body problem, these are:
♦ The validity of the planar restricted circular three-body problem,
♦ The possible values of the mass parameter ,and
♦ The practical form of the equations of motion
We then developed some important realistic applications of the third body problem in the solar system. These applications are divided into two categories, the first category is devoted to the planetary dynamics, for which we consider:
1- The Trojan Asteroids.
2- Orbit-Orbit Resonances for:
a-Hilda and Thule asteroids.
b-Pluto/Neptune.
While, the second category, is devoted to the applications of the restricted problem for equipotential surfaces of the two-body problem. |
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Supervisor |
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dr.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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1433 AH
2012 AD |
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Co-Supervisor |
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Dr. Magdy AL-Saftawy |
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Added Date |
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Saturday, April 14, 2012 |
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Researchers
| نوره صائل الحارثي | Al-Harthi, Noura Sail | Researcher | Master | |
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