الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
1. The rotational motion of a rigid body close to Lagrange’s gyroscope is investigated in Chapter (1) under the influence of NFF, EF, GM, and PM.
2. The small parameter has been inserted into the solutions procedure, according to some restrictions on the angular velocity, applied torques, and forces.
3. The governing EOM are transformed into a system of two second-order nonlinear differential equations with 2 DOF.
4. The application of the AT in this problem, explored that the attained new results generalize the results of the works in [65] (in the absence of the GM, NFF and EF) and [66] (without consideration of NFF and the first two projections of the GM).
5. The AT has been employed in Chapter (2) to obtain the averaging system of the EOM.
6. A number of applications have been studied and discussed according to the corresponding solutions the averaging system.
7. These solutions have been drawn to demonstrate the influence of various values of the applied forces and moments on the investigated motion.
8. The achieved results generalize some of the previous works when the NFF and the point charge are reduced, in addition to the absence of the spring, e.g. [68,70,71] and [72].
9. The optimal control and the minimum time have been established in Chapter 3.
10. Euler-Poisson’s type of motion is considered as a controlled motion taking into account the dependency of angular momentum on time.
11. Two cases for the RB motion have been examined under certain conditions related with kinetic energy and angular momentum of the body.
12. The comparison between the obtained results with the previous one in [45] shows high consistency between them for a null value of GM.
13. These results can be considered as generalization of those which were obtained in the previous works.
14. The differences between our obtained results and the previous ones have been represented graphically to reveal the importance of GM.
15. A time quasi-optimal slowing problem for the rotation of a dynamically asymmetric RB in a resistive medium under the influence of a GM and a small control torque is examined in Chapter 4.
16. The control optimal decelerating law for the RB rotation is achieved, in which the study of quasi-stationary trajectories is carried out.
17. The obtained novel results are depicted to determine the GM favourable impact on the functions of the angular momentum and the kinetic energy, as well as the square module.
18. The terms of “optimal” and “semi-optimal” slowing are varied when different values of the controlled torque dimension are selected.
19. A case of small perturbation is studied to reveal the action of the control torques on the body motion and it is compared with the unperturbed one.
20. The achieved results are graphed for various values of the GM, identifying number, and perturbed parameter.
21. These results generalize those which were obtained in [48] for the zero value of the GM.
22. Computer codes are used to represent the obtained solutions of this thesis graphically and to show the good effect of the different moments, NFF, and EF on the motion.