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Coordinate Systems
The significance of coordinate systems is their ability to enable numerical calculations of symbolic equations. After all, modeling of aerospace vehicles finds its fulfillment in simulations, and computers can only chew on numbers and not on symbolic letters.
As you build your simulations, you will require many types of coordinate systems. Let me list those that are the most important ones: heliocentric, inertial, Earth, perifocal, geographic, local level, velocity, body, stability, aeroballistic, and relative wind coordinate systems. Others arise as applications require it: gimbal, sensors, nozzle, target coordinate systems, etc.
With such a confounding multitude it is understandable that order had to be established by standardization. In Germany, the LN Standard 93002 has been in use for many years. The U. S. has lagged behind. In the past I had to rely on a sole U. S. Navy document3 for aeroballistic modeling. In 1992 AIAA published, in collaboration with the American National Standards Institute, the Recommended Practice for Atmospheric and Space Vehicle Coordinate Systems.4 Of course, over the years, many textbooks have served as references as well: Etkin,5 Bate et al.,6 Britting7; and more recently, Pamadi,8 Vallado,1 and Chatfield.9
As we make the transition from frames to coordinate systems, the preferred coordinate system, defined earlier, will play an important role. If a triad has been defined for a frame, it is most convenient to pick from the infinite number of associated systems one that lines up with the base vectors.
Just like frames refer to each other—establishing their relative position— coordinate systems are related by coordinate transformations. Let us briefly review (see Chapter 2): coordinates are ordered algebraic numbers that are related to the Euclidean space by coordinate systems and relabeled by coordinate transformations. We employ only right-handed Cartesian coordinate systems. Before we detail the most important coordinate systems and their transformations, we will discuss the properties of coordinate transformation matrices.
