Reference frames and transformations
When formulating and solving problems in flight dynamics, a number of frames of reference (coordinate axes) must be used for specifying relative positions and velocities, components of vectors (forces, velocities, accelerations etc.) and elements of matrices (aerodynamic derivatives, moments and products of inertia, etc.). The equations of motion may be written from the standpoint of an observer fixed in any of the reference frames, the choice being a matter of convenience and preference, and formulae must be available for transforming quantities of interest from one frame to another. For example, in an interplanetary space flight mission, one might need Earth – fixed axes, target-fixed axes, vehicle-fixed axes, and axes fixed to the distant stars. In atmospheric flight, we commonly use Earth-fixed axes, vehicle-fixed axes, trajectory-fixed axes, and atmosphere-fixed axes. The references frames needed for subsequent analytical developments are defined in the following, and a suitable system of notation is introduced.