Why is curvature independent of speed KmagnitudedTds this me

Why is curvature independent of speed?

K=magnitude(dT/ds) this measures how much the unit tangent changes given a small change along the curve. Why is it independent of speed? isn\'t the small change of the curve based on the speed?

Solution

First, I would like to refer http://web.cs.iastate.edu/~cs577/handouts/curvature.pdf in which there is a detailed analysis on curvature of arbitrary speed curves (section 2). In their notation T\'=dT/ds which is shown to be indeed dependent on the speed v (Eq. 5) . So, I am not sure about what you are asking for. One thing, that is to be understood is that curvature is a property of the curve. So, it will not change how we look at it, i.e. how we parameterize it.