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.