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

Find the value of given equations in polynomial , If α & ß are the zeroes ...

If α & ß are the zeroes of the polynomial 2x 2 - 4x + 5, then find the value of a.α 2 + ß 2   b. 1/ α + 1/ ß  c. (α - ß) 2 d. 1/α 2 + 1/ß 2    e.  α 3 + ß 3 (Ans:-1, 4/5 ,-6,

VECTORS, OQRS IS A QUADRILATERAL SUCH THAT OQ= -6,3 OR= -3,7 AND OS= 1,5. T...

OQRS IS A QUADRILATERAL SUCH THAT OQ= -6,3 OR= -3,7 AND OS= 1,5. T IS ON OQ SUCH THAT OT: TQ= 1:2 PROVE THAT QRST IS AA PARALLEGRRAM

How many cubic feet of steel is require to construct, A spherical holding t...

A spherical holding tank whose radius to the outer surface is 10 feet is constructed of steel 1 inch thick. How many cubic feet of steel is require to construct the holding tank? R

Operation on polynomial, Perform the denoted operation for each of the foll...

Perform the denoted operation for each of the following.  (a) Add 6x 5 -10x 2 + x - 45 to 13x 2 - 9 x + 4 .   (b) Subtract 5x 3 - 9 x 2 + x - 3 from       x 2+ x +1.

Algebra, how to solve algebra

how to solve algebra

The equation of the tangent, Consider the function f(x) = 2x 2 + 1. Find ...

Consider the function f(x) = 2x 2 + 1. Find the equation of the tangent to the graph of f(x) at x = 2. [NOTE: when calculating f'(2), use first principles.

Factoring by grouping, Factoring By Grouping It is a method that isn't ...

Factoring By Grouping It is a method that isn't utilized all that frequently, but while it can be used it can be somewhat useful. Factoring by grouping can be nice, however it

Linear programming, Chelsea has been facing some financial problems which e...

Chelsea has been facing some financial problems which even caused her daily expenses for food, at the same time, she hasn''t receive the money from the bank loan yet. Therefore, sh

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