Qualitative spatial reasoning has many applications in such diverse areas as natural language understanding, cognitive mapping, and reasoning about the physical world. We address problems whose solutions require integrated spatial and dynamic reasoning. In this paper, we present our spatial representation, based on the extremal points of objects, and show that this representation is useful for modeling the spatial extent, relative positions, and orientation of objects, and in reasoning about changes in spatial relations and orientation due to the translational and rotational motion of objects. Our theory has been implemented to support a magnetic fields problem solving application using the QPC and QSIM systems for qualitative modeling. The issues encountered in integrating spatial and dynamic reasoning in the context of these systems are also discussed.