Let x: I → R2 be a path of class C2 that is not a straight line and such that x’(t) 0. Let
This is the path traced by the center of the osculating circle of the path x . The quantity ρ = 1/κ is the radius of the osculating circle and is called the radius of curvature of the path x. The path e is called the evolute of the path x. Exercises 20–25 involve evolutes of paths.
Assuming κ’(t) 0, show that the unit tangent vector to the evolute e(t) is parallel to the unit normal vector N(t) to the original path x(t).
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.