In this work, we study the phase space geometry of the Barbanis model and explore its applications in physics and chemistry. Our analysis relies on tools from dynamical systems theory, such as the method of Lagrangian Descriptors, which provides a modern approach to unveiling the underlying geometric structures that govern the dynamics. In addition, we employ more classical techniques, including Poincare surfaces of section. By combining these methodologies, we investigate transport phenomena within the classical as well as the rotating Barbanis model, a central aspect for understanding how trajectories evolve, interact, and redistribute across phase space in both models. Such insights are of fundamental importance not only for a deeper comprehension of the theoretical foundations of dynamical systems, but also for practical applications in areas such as reaction dynamics in chemistry, celestial mechanics, and molecular physics.