The main objective of this paper is to present a novel approach for dynamic modeling of manipulators mounted on a flying base. The most significant challenges addressed in this research can be summarized as follows: 1) Determining an appropriate formulation for computing the generalized forces of the system, including both the active forces generated by the actuators and the passive forces arising from the constraints governing the system. 2) Defining a desired trajectory for the flying base that incorporates not only the desired position but also the desired orientation. 3) Developing an automatic and systematic dynamic modeling framework such that increasing the number of links in the robotic manipulator or the flying base does not impose any limitation on the derivation of the system’s equations of motion. 4) Arranging the motors installed on the flying base in a manner that enables arbitrary motion in three-dimensional space. To overcome these challenges, the overall robotic structure—comprising the flying base and the mounted manipulator is first decomposed, through a fully systematic procedure, into a specified number of substructures. The dynamic equations of motion of each substructure (which can be regarded as an open kinematic chain with a moving base) are then derived using the recursive Gibbs–Appell algorithm. Subsequently, by appropriately combining the equations of motion of these robotic chains, the kinetic equations of motion of the complete system are obtained, explicitly accounting for the mutual dynamic interactions between the flying base and the robotic manipulator.