Reparametrization to find arc length


by llooppii
Tags: calculus, parametric equations, reparametrization, vectors
llooppii
llooppii is offline
#1
Sep21-11, 08:53 PM
P: 8
1. The problem statement, all variables and given/known data

Reparametrize the curve with respect to arc length measured from the point where t=0 in the direction of increasing t.

r(t) = [e^(2t)cos(2t)]i+2j+[e^(2t)sin(2t)]k


2. Relevant equations

i know that the derivative of the arc length with respect to t = magnitude of the derivative of r(t).

3. The attempt at a solution

I found the derivative and found the magnitude, but am basically lost as of there.
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
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lanedance
lanedance is offline
#2
Sep21-11, 08:57 PM
HW Helper
P: 3,309
start by finding the arc length as function of t
icystrike
icystrike is offline
#3
Sep22-11, 05:17 AM
P: 439
Let s(t) be the arc length, and I'm sure Ur calculus textbook will have the formula of arc length..

icystrike
icystrike is offline
#4
Sep22-11, 05:25 AM
P: 439

Reparametrization to find arc length


In fact you can easily "derive" the formula with pythagorus theorem and riemman sum in mind.


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