Motion planning research has been successful in developing planning algorithms which are effective for solving problems with complicated geometric and kinematic constraints. Various applications in robotics and in other fields demand additional physical realism. Some progress has been made for non-holonomic systems. However systems with complex dynamics, significant drift, underactuation and discrete system changes remain challenging for existing planning techniques particularly as the dimensionality of the state space increases. This thesis develops a novel motion planning technique for the solution of problems with these challenging characteristics. The novel approach is called Path Directed Subdivision Tree Exploration algorithm (PDST-EXPLORE) and is based on sampling-based motion planning and subdivision methods. PDST-EXPLORE demonstrates how to link a planner with a physical simulator using the latter as a black box, to generate realistic solution paths for complex systems. The thesis contains experimental results with examples with simplified physics including a second order differential drive robot and a game which exemplifies characteristics of dynamical systems which are difficult for planning. The thesis also contains experimental results for systems with simulated physics, namely a weight lifting robot and a car. Both systems have a degree of physical realism which could not be incorporated into planning before. The new planner is finally shown to be probabilistically complete.