Curvature Formula

May 2016
368
5
NYC
Find curvature given r (t) = e^t*cost i + e^t*sint j.

There are two formulas but I was told to avoid using the formula that does not involve the cross product when no value for the parameter t is given.

Formulas:

1. K = ||r'(t) X r"(t)||/||r'(t)||^3

2. K = ||T' (t)||/||r'(t)||

Which formula is "easier" to apply in this case and/or in most cases? I was told to apply formula (1) for polynomials. What about for problems involving e^t, lnx and trigonometric functions?
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey USNAVY.

It should depend on whether you have T(t) and r(t) or just r(t).
 
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May 2016
368
5
NYC
Hey USNAVY.

It should depend on whether you have T(t) and r(t) or just r(t).
I gave up on this question after several attempts to solve it. I came very close to getting the right answer yesterday but failed. My answer is K = e^(-t)/(cos t)^2. The right answer is (sqrt {2}/2)(e^(-t). Can you solve it step by step?I want to see the proper steps and use your solution to solve similar questions in my textbook.
 
Last edited:

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
We usually get the poster to show their working before we give them more advice.
 
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