A direct trajectory optimization method that uses neural network approximation methods is presented. Neural networks are trained to approximate objective functions and vehicle dynamics. The neural network method reduces computational requirements by removing the need for collocation and providing fast computation of gradients. The method has been shown to significantly reduce computational costs while resulting in trajectories comparable to direct collocation and pseudospectral methods. Since the neural networks readily provide accurate computation of gradients, it removes the need for formulating analytical gradients, so the method is more easily extended to different types of applications with different objective functions and constraints. In previous work, the method was applied towards trajectory optimization of single or multiple UAVs with fixed, downward facing cameras in order to maximize surveillance of a ground target. In this paper the method is extended to optimize trajectories for a UAV equipped with a gimbaled camera, and more complex constraints on the vehicle trajectory are investigated.