In recent years artificial intelligence (AI) and machine learning techniques have found immense success in the fields of pattern recognition, classification, and data analytics. These techniques also have shown to provide viable means of controlling and modeling of uncertain, nonlinear dynamic systems. However, such techniques have not yet found widespread adoption in controls due to concerns in reliability, interpretability, and stability. In the past, much of the work in the field of dynamics has been based on well understood physical principles (i.e., Newtonian, Lagrangian, and Hamiltonian mechanics), while control has been model-based, as they adequately address the aforementioned concerns. The presented work attempts to retain the benefits of both AI and physics-based control, by using recently developed neural networks that incorporate Lagrangian mechanics into the learning scheme to create an inverse dynamic model of a quadcopter. The inverse dynamic model is utilized in developing a control scheme that is shown to learn the changes in system parameters effectively in an online fashion. The proposed control scheme is validated with the help of extensive simulation studies performed on a quadcopter, and the performance is compared to simple adaptive control for cases where mass and inertia change in flight for complex trajectories.