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

Elimination technique of linear equations, What is the Elimination techniqu...

What is the Elimination technique of Linear Equations?

Correlation and regression, Correlation and Regression Correlation ...

Correlation and Regression Correlation CORRELATION is an important statistical concept which refers to association or interrelationship among variables. The reasons of

Slope, #question.Find the slope of the line that passes through (7, 3) and ...

#question.Find the slope of the line that passes through (7, 3) and (9, 6). Simplify your answer and write it as a proper fraction, improper fraction, or integer. .

Modeling , A plastic manufacturer has 1200 boxes of transparent wrap in sto...

A plastic manufacturer has 1200 boxes of transparent wrap in stock at one factory and 1000 boxes at his second factory.The manufacturer has order for this product from 3 different

How are Indian customers visiting Shoppers’ Stop any differe, How are India...

How are Indian customers visiting Shoppers’ Stop any different from customers of developed western countries?

Right angle trigonometry, use the Pythagorean Theorem to find the length of...

use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. give an exact answer with a rational denomina

General solution to a differential equation, The general solution to a diff...

The general solution to a differential equation is the most common form which the solution can take and does not take any initial conditions in account. Illustration 5: y(t) =

Quadratic equation, If roots of (x-p)(x-q) = c are a and b what will be th...

If roots of (x-p)(x-q) = c are a and b what will be the roots of (x-a)(x-b) = -c    please explain? Ans) (x-p)(x-q)=c x2-(p+q)x-c=0 hence,   a+b=p+q  and      a.b=pq-c

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