Modelers often prefer Cartesian Coordinate Frameworks
Dynamics equations can be “simplified”so that they are cheaper computationally. Velocity and acceleration components generally do not contain trigonometric functions.
In Cartesian real world systems straight lines are linear functions.
- Shortest distance paths are straight lines.
- The Euclidean metric requires only a square root operation.
In other coordinate systems minimum distance paths may be non- trivial to compute.
Segments of ellipses lead to elliptic integrals.
- Shortest path on the surface of an ellipsoid is a geodesic (not an arc segment of an ellipse).
The Earth and its natural environment are modeled with an ERM and a SNE.
- In this model shortest distance (or time) paths are not unique, and
- Almost always are not geodesics or straight lines.