# Curve parametrizations

• December 2nd 2009, 05:38 AM
SirOJ
Curve parametrizations
Find the vectors
T, N and B as well as the curvature  and the torsion  for the curve

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

I calculated e^t = (4/3)s.. Is there any way i can get t = "something" from this equation because i need to parametrize the above curve in terms of the arc length "s"
• December 2nd 2009, 06:21 AM
HallsofIvy
Quote:

Originally Posted by SirOJ
Find the vectors
T, N and B as well as the curvature  and the torsion  for the curve

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

I calculated e^t = (4/3)s.. Is there any way i can get t = "something" from this equation because i need to parametrize the above curve in terms of the arc length "s"

Well, yes! If $e^t= (4/3)s$ then t= ln((4/3)s which you can, if you like, write as t= ln(s)+ ln(4/3)= ln(s)+ ln(4)- ln(3).