M310 L09 13'3 Arc Length and Curvature

1
M310 L09 13.3 Arc Length and Curvature
2
13.3 1 Arc Length of a Helix
Find the arc length from (1,0,0) to (1,0,2pi)
3
Arc Length is Independent of Parameter
4
13.3 2 Reparametrizing Arc Length
Continue 1 and find the arc length from
(1,0,0)
5
Curvature
6
13.3 3 Curvature of a Circle of Radius a
7
Curvature in Terms of Two Derivatves
8
13.3 TRICKS
There are two simple ways to give a manageable
problem of calculating arc length (1) the
square of the magnitude of r' may be a perfect
square. (2) part of the radicand may be factored
out of the radical, and the resulting radicand
used as a new variable u for integral
substitution.
9
13.3 4 Curvature of a Twisted Cubic