*``Flight dynamics courses are exiting to the student and to
the teacher, except for the initial portion where the equations of
motion are derived.''*

--S. Pradeep

Many references derive the equations of motion for a rigid airplane . This paper will not duplicate the derivation.

The flight simulator ultimately uses the equations of motion to calculate the time derivatives of the state variables. As such, this paper presents the equations in state variable form, where the equations are solved for the time derivatives.