We are all familiar with a body traversing uniformly ( or non uniformly ) along the circumference of a circle. We get nice relations because of the symmetry of the figure and the distance between every point on the trajector and the centre of the circle remains constant.
The ellipse is also quite a symmetric figure however the body traversing does not move equi distantly from the centre of the ellipse. Due to this I am unable to derive any kind of a function that can define the motion of a body moving along an elliptical path.
Planetary motion is elliptical and I am familiar with how the displacement is derived in that case, but that takes help from the Newton's law of gravitation, which gives us an extra relation to attempt the problem. However how must one approach the problem in a general case?
Can someone please help me derive the displacement and the velocity functions for a body moving uniformly on an elliptical trajectory? What properties of the ellipse can be exploited the derive the same?
Any kind of help or guidance would be appreciated. Thank you in advance!