In recent years, dynamically stable platforms that move on spherical wheels, also known as BallBots, gained popularity in the robotics literature as an alternative locomotion method to statically stable wheeled mobile robots. In contrast to wheeled platforms which do not have to explicitly be concerned about their balance, BallBot platforms must be informed about their dynamics and actively try to maintain balance. Up until now, such platforms have been approximated by simple planar models, with extensions to three dimensions through the combination of decoupled models in orthogonal sagittal planes. However, even though capturing certain aspects of the robot’s motion is possible with such decoupled models, they cannot represent inherently spatial aspects of motion such as yaw rotation or coupled inertial effects due to the motion of the rigid body. In this thesis, we introduce a novel, fully-coupled 3D model for such spherical wheeled balancing platforms. We show that our novel model captures important spatial aspects of motion that have previously not been captured by planar models. Moreover, our new model provides a better basis for controllers that are informed by more expressive system dynamics. In order to establish the expressivity and accuracy of this new model, we present simulation studies in dynamically rich situations. We use circular paths to reveal the advantages of the new model for fast maneuvers. Additionally, we introduce new inverse-dynamics controllers for a better attitude control and investigate within simulations the capability of sustaining dynamic behaviors. We study the relation between circular motions in attitude angles and associated motions in positional variables for BallBot locomotion.