As others suggested Kinematics is really important in representation of airplane motion and it can be expressed by Euler Angles, Transformation Matrices and different reference frames.
As you asked this question for maintenance application, it seems that the kinetics is also important for you, State-Space representation is a useful approach to present the equations of motion in matrix form. There are many books on airplane flight dynamics discussed on both kinetics and kinematics of airplanes. I can suggest to study "Airplane Flight Dynamics and Automated Flight Controls I-II " written by John Roskam.