Derivation of aircraft, linear state equations from implicit nonlinear equations

The classical approach to deriving linear models of aircraft dynamics is cumbersome because of the lack of a formal algebraic framework. A new point of view is taken to provide a streamlined derivation for the linear state equations by using some formal mathematical tools. These tools include matrix calculus and implicit differential equations. The linear equations derived differ slightly from the conventional linear aircraft equations and are believed to be more accurate. They have been compared with linear equations derived by numerical linearization and found to agree to several decimal digits