This disclosure relates to modeling and visualization of vibration mechanics in residual space, and includes systems and methods for vibrational analysis. In one embodiment, a method includes acquiring, by at least one sensor, vibrational data and an operational mode of rotating equipment. The method may then proceed with determining, by an equipment controller communicatively coupled to the sensor, at least one vibrational vector based on the vibrational data. The method may determine, by the equipment controller and based on a model, an expected vibrational vector for the operational mode. The method may calculate, by the equipment controller, a residual vector as a difference between the vibrational vector and the expected vector. The method may also determine, by the equipment controller, at least one abnormality associated with the rotating equipment based on the residual vector. The method may display a graph representing boundaries of a region of allotted residual vectors and a point representing the residual vector.