Normal and centrifugal force for arbitrary curves

[Gavroy]

Hi, i have a curve g:[0,t]->IR² with g(t)=(x(t),y(t)) in a homogenous gravitational field and i want to look at a ball rolling down this curve. therefore i want to derive some equations in order to calculate the normal force and the centripetal force at each point of this curve in order to see where the ball "leaves" the curve. therefore i am looking for an equation that gives me both forces just by using the parametrization of my curve. is there an equation for this?

 

[rcgldr]

This might help, the radius of curvature for a parametric curve is:

radius(t) = ( (x'(t))² + (y'(t))² )^3/2 / | (x'(t) y''(t)) - (y'(t) x''(t)) |