Looks like your assumptions are a constant radius and two dimensional motion. Does your methodology backsolve for the center based upon these assumptions? Is that correct?
roll - gybe,
If I had assumed a constant radius I would have analyzed the simple case of a circle where the radius is constant.
It should be clearly understood that this is not the approach taken.
Let me outline briefly the basic methodology.
For a continuous curve one can define at any point the curvature and its inverse, the radius of curvature, the latter also referred to as instantaneous radius of curvature.
If the curve is known as a mathematical function than curvature and radius of curvature can be calculated, albeit resulting usually in rather complex expressions.
In this particular analysis I used a 2 or 3 segment mathematical model for the golf swing. Hence the clubhead trajectory can be derived as a mathematical function.
Once the trajectory known mathematically I can than derive the instantaneous radius at any point and hence also determine the locus of the instantaneous centers.
As you can see from above there is no assumptions of any kind except for the curve to be continuous and restrained to 2 dimensions.
Hope this helps, if not, simply ask more questions.
