# Equations of Motion and State-Space Realizations for Aircraft and Rotorcraft

*It seems that every textbook uses different sign conventions and approximations to derive the 6-DOF equations of motion for aircraft, linearized about the trim condition. In an effort to minimize the number of approximations required to build a state-space realization and shed light on the required approximations for linearization, I wrote this document. It includes the fully nonlinear 6-DOF equations of motion, the linearized equations of motion, a general state-space formulation, a modified state-space formulation for applications where the small angle approximation does not hold, and a linear formulation for control system development. This formulation is appropriate for aicraft and rotorcraft, and does not neglect any stability and control derivatives like most textbooks do. I hope someone finds this as useful as I have found it to be!*