Notes for 11.5 - The sharper the curve, the greater the...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Calculus III – Section 11.5 – Arc Length and Curvature Theorem 11.6 If C is a smooth curve given by k t z j t y i t x t r ) ( ) ( ) ( ) ( + + = on the interval [ ] b a , , then the arc length of C on the interval is [ ] [ ] [ ] = + + = b a b a dt t r dt t z t y t x x 2 2 2 2 ) ( ' ) ( ) ( ) ( . Example: #4 #8
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Curvature Let C be a smooth curve (in the plane or in space) given by r (s), where s is the arc length parameter. The curvature at s is given by ) ( ' s T ds dT K = = OR for a general parameter t 3 ) ( ' ) ( " ) ( ' ) ( ' ) ( ' t r t r t r t r t T K × = = . Curvature is basically a measure of how sharply a curve bends.
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The sharper the curve, the greater the curvature. Notice that you are just calculating the magnitude of the rate of change of the unit tangent vector with respect to the arc length s. Use the version of the curvature formula that is most convenient for your problem. Example: #24 #34...
View Full Document

This note was uploaded on 01/13/2012 for the course MATH 2574 taught by Professor Pamelasatterfield during the Spring '12 term at NorthWest Arkansas Community College.

Page1 / 2

Notes for 11.5 - The sharper the curve, the greater the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online