The development of a dynamic model for control purposes of an Unmanned Aerial Vehicle (UAV) carrying a delta-manipulator for force exertion is the subject of this article. The floating base of the manipulator due to its attachment to the UAV dictates the need to account for the transfer of the reaction force and torque vector from the manipulator's base to the UAV, and in a reverse manner, the transfer of the translational and angular velocity and acceleration vector from the UAV to the manipulator. The nature of the closed-kinematic chain of the delta-manipulator necessitates its dynamics approximation by three single Degree of Freedom arms which are kinematically-constrained thru its moving platform. The controller for the arm relies on a computed-torque framework, while the UAV's PD-controller accounts for the instantaneous displacement of the manipulator's center-of-gravity with respect to its aerodynamic point of pressure. Gazebo-based simulation studies are provided to demonstrate the effectiveness of the suggested control scheme.