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

Square and square root., the value of square root of 200multiplied by squar...

the value of square root of 200multiplied by square root of 5+

Quadratic equation, can anyone explain me the concept of quadratic equation...

can anyone explain me the concept of quadratic equation?

Linear programming, what is the advantage of dual linear problem programmin...

what is the advantage of dual linear problem programming when we maximize profit then what is need to minimize cost of the same problem

Probability, TWO PERSONS A AND B AGREE TO MEET AT A PLACE BTWEEN 11 TO 12 N...

TWO PERSONS A AND B AGREE TO MEET AT A PLACE BTWEEN 11 TO 12 NOON.  THE FIRST ONE TOARRIVE WAITS FOR 20 MIN AND THEN LEAVE. IF THE TIME OF THIR ARRIVAL BE INDEPENDET AND AT RNDOM,T

Determine the approximate raw act score, Using the same mean and standard d...

Using the same mean and standard deviation as mean m = 20.1 and a standard deviation s = 5.8. Joe was informed that he scored at the 68 th percentile on the ACT, what was Joe's ap

Definition of laplace transforms, You know that it's all the time a little ...

You know that it's all the time a little scary while we devote an entire section just to the definition of something. Laplace transforms or just transforms can appear scary while w

Describe the properties of inequalities, Describe the Properties of Inequal...

Describe the Properties of Inequalities ? Postulate In comparing two quantities, say a and b, there are exactly three possibilities. (1) a is less than b. (a b)

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