Attitude Determination

A final subject of importance is the fundamental problem of kinematics of flight vehicles. In six-degree-of-freedom (DoF) simulations the application of Euler’s law renders the differential equations of body rates. More precisely, the solution of the differential equations yields the angular velocity vector of the vehicle frame В wrt the inertial frame I, expressed in body coordinates [wBI]B. Specialists call them the p, q, r components of

[coBIf = [p q r]

The fundamental problem states as follows: Given the body rates [coBI]B, deter­mine the orientation of the vehicle wrt the inertial frame. The orientation can be expressed in terms of the rotation tensor, Euler angles, or quaternion. Because ori­entation is removed from angular velocity by integration, the solution will embody differential equations. I shall treat each of the three possibilities individually.