Frames and Coordinate Systems

Chapter 2 introduced frames and coordinate systems. Frames are models of physical references, whereas coordinate systems establish the association with Euclidean space. Both entities are important elements of aerospace vehicle dy­namics. Frequently, they are presumed to be the same, but I will maintain a carefiil distinction throughout this book, heeding TruesdelFs warning, quoted earlier, that frames should not be regarded as a synonym for coordinate systems.

This chapter will expand our understanding of these concepts. Important frames of reference, such as inertial, Earth, and body frames will be introduced. The triad of base vectors will emerge as a keystone to define their location and orientation. It will bridge the chasm between frames and coordinate systems with the so-called preferred coordinate systems.

Coordinate systems are the spider web of simulations, providing structure, di­rection, and focus. They structure the Euclidean space into application-specific associations, establish sense of direction, and focus on numerical solutions— the sustenance of any simulation. However, they can also lead to bafflement and mystification and may ensnare the careless user. (I once developed an air combat simulation that dealt with 24 different coordinate systems.) Clarity of definition is essential. We shall deal with a host of systems: inertial, Earth, geo­graphic, local-level, perifocal, velocity, body, gimbal, relative wind, stability, aero – ballistic, and some more—hopefully all of the coordinate systems you will ever need.