I suggest you view this problem in terms of 3D graphics and rotation matrices.

Think of the circle as centered at the origin in the x-y plane. In 3-space the x-y plane has z coordinate zero. Suppose you are viewing the circle from point (x,y,z) = (0,0,10). Now tilt and/or rotate the x-y plane in 3-space. Keeping your viewing point the same, the tilt/rotation will transform the circle into an ellipse. That transformation can be described using a 3x3 rotation matrix M. Coordinates on the circle will be transformed to coordinates on the ellipse by multiplying by the matrix M. I am not familiar with the physics, but I would think since the transformation is linear, the transformations of physical quantities such as velocity should be straightforward to calculate.

Here are two links that will introduce you to 3D graphics in a more general way: Brian Wyvill. Wikipedia on 3D projection.

I think these may be helpful to you because your other post on this subject says you have a photo of a tilted clock face. When you have a photo taken by a camera (or drawn by computer graphics) there is another transformation that comes into play: the perspective transform. That is, objects that are farther away from the camera appear smaller than objects nearer the camera. This means a tilted circle will not transform exactly into an ellipse. Ignoring the perspective transformation will introduce another set of errors into your calculations besides measurement errors. The above links describe the transformations involved and how to apply them using matrix methods.

The above links give you the full generality of 3D graphics, which can be daunting when you are first introduced to it. But the transformations turn out not so bad for this problem and if you are interested in this approach, I can help you work out an example.