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!
1. The stationary vector of point P when is
.
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: