Next: Control Variables Up: The Airplane Previous: The Local Coordinate System.

### State Variables

To represent the airplane at a point in time, the flight simulator uses a set of state variables. The state variables completely determine the state of the airplane. The flight simulator simulates the airplane's motion by calculating the time derivatives of the state variables, using the equations of motion. Using the time derivatives, it numerically integrates the state variables in real time.

The airplane exists in three dimensions; thus three state variables ( xc,yc,zc in a Cartesian system) determine the position of the CG, relative to a local or Earth-fixed coordinate system.

Three Euler angles ( ) or four quarternions ( e0,e1,e2,e3) determine the airplane's orientation relative to local axes; these are state variables.

In dynamics, the velocity (linear and angular) of a body is part of the state as well. Thus, the three components of linear velocity in body axes (u,v,w), and the three components of angular velocity in body axes (p,q,r), are state variables.

There are other state variables, as well. The mass of the airplane affects its dynamics, and the mass does change as the fuel burns. Thus, the mass of the fuel in the tanks in a state variable. The engine speed and manifold pressure are state variables. Additionally, other state variables can emerge as the complexity of the airplane model increases.

Next: Control Variables Up: The Airplane Previous: The Local Coordinate System.
Carl Banks
2000-08-11