I lost trying to find the osculating circle for the curve defined by r(t) = <sint, cost, -pi + t> at the point t=pi.
Ive calculated the radius of the circle to be 1 and I know I need to somehow use the unit normal vector at point t=pi, which is <0, 1/sqrt(2), 0> to solve for the osculating circle's centre, but I do not know how to do that.
Thans for your help!
2. I've got the normal unit vector as
3. The sum of these two vectors will yield the stationary vector of the center of the circle:
4. The tangent at the curve in P and the normal vector produce a plain in which the osculating circle must be placed. The equation of the tangent is: