TABLE OF CONTENTS Consider a coordinate system with a set of three orthogonal axes centered on the Earth's geometric center: the z-axis passes through the North Pole and the x and y axes are in the equatorial plane and where the x-axis is along the Greenwich meridian. Could you imagine this coordinate system being used to locate objects on Earth? Imagine an aircraft approaching the Los Angeles Airport and identifying its location relative to this coordinate system as (-2499km, 2952km, 3528km); can an airport traffic controller in the tower guide this aircraft to land safely? Yes, it can be done but it will be cumbersome and most importantly counterintuitive. It would be more useful and more intuitive if the aircraft had identified its location by its coordinates relative to a Cartesian coordinate system centered at the tower or by its longitude, latitude and altitude. To be sure, the Earth center coordinate system we have just described is very useful but for other purposes.
In general, there is no unique set of axes to define an n-dimensional space since any set of n orthonormal vectors can be used to represent arbitrary n-dimensional vectors. As will be seen, it is convenient to favor a specific frame to represent vectors over other frames. For example, it is a nightmarish process, except for trivial cases, solving the Newton s angular momentum equations using a fixed frame system. However, it is much easier to solve these equations using a frame...
