Advances in machine autonomy hold great promise in advancing technology, economic markets, and general societal well-being. For example, the progression of unmanned air systems (UAS) research has demonstrated the effectiveness and reliability of these autonomous systems in performing complex tasks. UAS have shown to not only outperformed human pilots in some tasks, but have also made novel applications not possible for human pilots practical. Nevertheless, human pilots are still favored when performing specific challenging tasks. For example, transportation of suspended (sometimes called slung or sling) loads requires highly skilled pilots and has only been performed by UAS in highly controlled environments. The presented work begins to bridge this autonomy gap by proposing a trajectory optimization framework for operations involving autonomous rotorcraft with suspended loads. The framework generates optimized vehicle trajectories that are used by existing guidance, navigation, and control systems and estimates the state of the non-instrumented load using a downward facing camera. Data collected from several simulation studies and a flight test demonstrates the proposed framework is able to produce effective guidance during autonomous suspended load operations. In addition, variational integrators are extensively studied in this dissertation. The derivation of a stochastic variational integrator is presented. It is shown that the presented stochastic variational integrator significantly improves the performance of the stochastic differential dynamical programming and the extended Kalman filter algorithms. A variational integrator for the propagation of polynomial chaos expansion coefficients is also presented. As a result, the expectation and variance of the trajectory of an uncertain system can be accurately predicted.