Curvature - three dimensional space, Mathematics

Assignment Help:

Curvature - Three Dimensional Space

In this part we want to briefly discuss the curvature of a smooth curve (remind that for a smooth curve we require r′ (t) is continuous and r′ (t) ≠ 0 ).  The curvature measures how fast a curve is changing direction at a specific point.

There are various formulas for finding out the curvature for a curve. The formal definition of curvature is,

k = |d T/ ds|

in which  T stands for the unit tangent and s is the arc length. Remind that we saw in a preceding section how to reparameterize a curve to acquire it into terms of the arc length.

Generally the formal definition of the curvature is not simple to use so there are two alternate formulas that we can utilize. Here they are.

Κ = ||T' (t)|| /|| r' (t)||

Κ = || r' (t) * r''(t)|| /|| r' (t)||3

These may not be particularly simple to deal with either, although at least we don't need to reparameterize the unit tangent.


Related Discussions:- Curvature - three dimensional space

Definite integral, Definite Integral : Given a function f ( x ) which is c...

Definite Integral : Given a function f ( x ) which is continuous on the interval [a,b] we divide the interval in n subintervals of equivalent width, Δx , and from each interval se

Core concepts, what are the core concept of marketing

what are the core concept of marketing

Fractions, What fraction could you add to 4/7 to get a sum greater than 1

What fraction could you add to 4/7 to get a sum greater than 1

Method of disks or the method of rings, Method of disks or the method of ri...

Method of disks or the method of rings One of the simple methods for getting the cross-sectional area is to cut the object perpendicular to the axis of rotation.  Carrying out

The definite integral- area under a curve, The Definite Integ...

The Definite Integral Area under a Curve If there exists an irregularly shaped curve, y = f(x) then there is no formula to find out

Piecewise, x=±4, if -2 = y =0 x=±2, if -2 = y = 0

x=±4, if -2 = y =0 x=±2, if -2 = y = 0

Describe about parallel and perpendicular lines, Describe about Parallel an...

Describe about Parallel and Perpendicular Lines ? Parallel Lines : Parallel lines are coplanar lines (lines that lie in the same plane) that never intersect. The bl

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd