|
Document Type |
: |
Thesis |
|
Document Title |
: |
MOTION IN ORTHOGONAL CURVILINEAR COORDINATES: APPLICATIONS TO J2 GRAVITY PERTURBED MOTION OF THE EARTH’S ARTIFICIAL SATELLITES الحركة في الإحداثيات المنحنية المتعامدة: تطبيقات على حركة الأقمار الصناعية المقلقة بمجال الجذب التفلطحى J2)) للأرض |
|
Subject |
: |
Astronomy department |
|
Document Language |
: |
Arabic |
|
Abstract |
: |
In this thesis initial value problem for dynamical astronomy was established (to the first time) analytically and computationally using orthogonal curvilinear coordinates.
The initial value problem was treated with its two basic formations: coordinates and orbital elements.
For the analytical developments, expressions for the equations of motion, and the orbital elements were established symbolically for any orthogonal curvilinear coordinates. While for the computational developments, two algorithms were also established, which are:
1- Algorithm for the initial value problem of gravity perturbed trajectories of the space dynamics in terms of orthogonal curvilinear coordinates. 2- Algorithm for the classical orbital elements for gravity perturbed trajectories in terms of orthogonal curvilinear coordinates. The spatial case of the pure Kepler motion is also considered
Applications of the algorithms for the problem of final state prediction which is important in targeting, rendezvous maneuvers as well for scientific researches, were illustrated by numerical examples of some test orbits of different eccentricities.
The numerical results are extremely accurate and efficient in predicting final state for gravity perturbed trajectories as well as for the pure Kepler motion. Moreover, an additional efficiency of the algorithms is that, one can reach the desired accuracy using at most 70% of the number of steps that used for obtaining the reference final state solution. By this reduction, the step size becomes larger, hence minimizing the computational errors. Finally, the usage of the orthogonal curvilinear coordinates leads to a wonderful property which is, the variations of the transformed variables during the orbit are very small in comparison to the corresponding variations of rectangular variables , a property which produces more stable numerical integration procedure.
It should be mentioned that, by using orthogonal curvilinear coordinates the independent variables are only, changed which in turn produce transformations from three dimensional Cartesian space to another three dimensional space.
Finally, as a byproduct, general symbolic expressions for the collisionless Boltzmann equation of the stellar dynamics were also established and listed in Appendix A. |
|
Supervisor |
: |
1. Prof. Mohammed Adel Sharaf |
|
Thesis Type |
: |
Master Thesis |
|
Publishing Year |
: |
1433 AH
2012 AD |
|
Co-Supervisor |
: |
Dr. Majdy Al-Saftawy |
|
Added Date |
: |
Saturday, April 28, 2012 |
|
Researchers
| باسمة فارس الجهني | Al-Jehani, Basema Faris | Researcher | Master | |
|