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

Operations and properties, use an expression to write an expression with fi...

use an expression to write an expression with five 3s that has a value of 0

Problem of purchasing, story of faicing problem when customer purchasing a ...

story of faicing problem when customer purchasing a product

Determine the range of given algorithm, The division algorithm says that wh...

The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(

Example of fraction, Example  Reduce 24/36 to its lowest terms. 2...

Example  Reduce 24/36 to its lowest terms. 24/36=12/18=6/9=2/3. In the first step we divide the numerator and the denominator by 2. The fraction gets reduced

Prove gcd value, Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc f...

Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc for all c. (b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.

Evaluate the slope of the line, Evaluate the slope of the line: Examp...

Evaluate the slope of the line: Example: What is the slope of the line passing through the points (20, 85) and (30, 125)? Solution:            m = 125 -85/30-20 = 4

Find a minimum cost spanning arborescence rooted, Find a minimum cost spann...

Find a minimum cost spanning arborescence rooted at r for the digraph shown below, using the final algorithm shown in class.  Please show your work, and also give a final diagram w

Infinite limits, Infinite Limits : In this section we will see limits who...

Infinite Limits : In this section we will see limits whose value is infinity or minus infinity.  The primary thing we have to probably do here is to define just what we mean w

Shares and dividend, A man buys rs50 shares of a company paying 12% of divi...

A man buys rs50 shares of a company paying 12% of dividendat premium ofof rs10 find market value of 320 shares and profit%

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