## sphere## Example for spherical coordinatesOne possible transformation from spherical coordinates (r,φ,ϑ) to cartesian coordinates (x,y,z) is: where: where: ## Geodetic distanceMy current try is: Length is defined to be: So if , then: The usual definition of "distance" is "minimum length", so try to find the minimum: -> min
where: And x, y, z as above, but with (r,φ,ϑ) being functions of t. So the extremum is determined by: I'm not sure how to stay ON the sphere with the curve. And so: After dropping the square root (is that safe?), one gets: How to stay on the surface of the sphere? ## Spherical AnglesThe Where A is the area on the surface of the sphere enclosed by beams from the center to the object. This is so that: Author: Danny (remove the ".nospam" to send) Last modification on: Sat, 04 May 2024 . |