I am confused why the acceleration doesn't point to the center of the ellipse or one of the focus, since it moves in circular motion. Shouldn't the acceleration be just in the radial direction
What is φ in your equations? I'm wondering if it would help to express x and y as functions of time. I did a web search and found a paper for ellipse with constant speed, but they're asking $16.00 to download it, and it's possible that the paper doesn't come up with an actual solution.This is indeed very difficult to solve.
Here is the link (maybe you can find this elsewhere). I did a search for "ellipse parametric constant speed" to search for articles, and this seemed to be the only one that could have a solution. It's from a math magazine article, archived at this web site.Which paper is it? Maybe I can download it via my university account.