Muslim-Christian Relations in the Era of Prophet Muhammad: Review of Najrān Delegation’s Case in Modern Context

Muslim–Christian relations are as mature as Islamic history itself. Historical evidences state the first interaction of Muslims and Christians occurred in 5th year after nabuwwah (615 AD) when Muslims migrated to Ḥabshah (Abyssinia) and second contact was established after immigration of the Holy Prophet (PBUH) to Madinah. After getting socio-political stability in 8th hijrī (629 AD), Muhammad (PBUH) sent letters and ambassadors to different statesmen and religious leaders to spread the Islamic Mission and Message globally. One letter was also sent to the chief Bishop of Najrān. In response, the chief Bishop of Najrān accepted the invitation and personally came to meet the Prophet (PBUH) with his reputed delegation. The beloved Messenger (PBUH) warmly welcomed this delegation. As a result, the peace agreement was reached after some theological debate and discussion. Later on, throughout history, the relations between Muslims and Christians have been in situation of up and down. It’s also a fact that over the centuries, the Muslims-Christians relations had sometimes been one of enmity, sometimes one of rivalry, competition, and encounter. In spite of it, the Najrān’s delegation case has a historical significance in Muslim-Christian relations in the literature of both religions. Therefore, in this study efforts were made to explore the event of Najrān delegation as theological foundations for Muslim-Christian relations in times of the Holy Prophet (PBUH) and how can we get benefit from it in modern era. Moreover, this study perceives that the case of Najrān delegation was the first practical interaction between Muslims and Christians of that age. Hence, we could get benefit from it with its modern applications and interpretations. The analytical, comparative and historical approaches have been adopted in this study with qualitative paradigm. I compared and analysed the case in Islamic and Christian context and then gave recommendation for its application.

Dynamics Numerical Optimization and Control of Dynamic Soaring Maneuvers for a Morphing Capable Unmanned Aerial Vehicle

Dynamicsoaringisaversatilemaneuverexecutedtoacquireenergyavailable in the atmospheric wind shears. For UAVs, dynamic soaring maneuvers have mostly been confined in literature to fixed configurations. In order to analyzetheextenttowhichdynamicsoaringisinfluencedbydifferentmorphologies, aninnovativeconceptofintegratingdynamicsoaringwithmorphingcapabilities is introduced in this research. Through simulations, two major studies were performed. One of them analyzed the impact of span morphology and the other of sweep morphology on dynamic soaring parameters. An Unmanned Air Vehicle(UAV) with standard wing-tail configuration is considered. The aerodynamic modeling is based on empirical estimation procedure duly validate dwit numerical Vortex Lattice Method(VLM).Three-dimensional point-mass UAV equations of motion and nonlinear wind gradient profile are used to model the flight dynamics. The trajectory optimization problem is formulated as an optimal control problem using hp-adaptive Guassian quadrature collocation technique. Optimal soaring trajectories are generated for both morphologies. Parametriccharacterizationofthekeyperformanceparametersisperformed to determine the optimal platform configuration during various phases of the maneuver. The comparison of morphing ability during flight is compared with its fixed-wing counterpart. Simulation results demonstrate the benefits of extending soaring maneu vers to morphing configurations and its viability for onboard utilization. Results indicate 15% lesser required wind shear by the proposed span morphology and 14% lesser required wind shear by the proposed sweep morphology, in comparison to their respective fixed wing counterparts. This shows that the morphing UAVcanperformdynamicsoaringinanenvironment,wherefixedconfiguration UAVs might not, because of lesser available wind shears. Apart from this, span morphology reduced drag by 15%, lift requirement by 11% and angle of attack requirement by 20%, whereas increased the maximum velocity by 6.2%, normalized energies by 9% and improved loitering parameters (approximately 10%), in comparison to fixed span configurations. Similarly, sweep morphology guaranteed 20% drag reduction, 16% lesser angle of attack requirement and improved loitering performance over the fixed sweep configurations. The stability analysis of the nonlinear system along the optimal trajectory is then performed utilizing both linear (Floquettheory) and nonlinear (Contraction theory) techniques. Stability of dynamic soaring orbits is important since the trajectories can get disturbed by a strong gust or crosswinds causing the UAV to veer off-course. Although control system can be designed, a stable orbit can reduce the control effort and power. The problem of analyzing stability is treated from the context of a periodic coefficient system. The stability analysis revealed that a closed-loop control is necessary as the system dynamics are inherently unstable. AgeometricnonlinearcontrollabilityanalysisofUAVunderdynamicsoaring conditions is then performed. To achieve such an objective, the state-of-theartmathematicaltoolsofnonlinearcontrollabilityareutilized. Thecontrollability of a flying vehicle along that optimal soaring trajectory is analyzed. More im portantly, the geometric nonlinear controllability characteristics of generic flight dynamics is analyzed in the presence and absence of wind shear to provide a controllability explanation for the role of wind shear in the physics of dynamic soaring flight. It is found that the wind shear is instrumental in ensuring controllability as it allows the UAV attitude controls (pitch and roll) to play the role of thrust in controlling the flight path angle. The presented analysis represents a controllability-based mathematical proof for the energetics of flight physics.