- #1
DameLight
- 24
- 0
Hi,
I am taking Calc III, but I am having a hard time understanding some of the concepts. Right now I am struggling with understanding the curvature of a line. What I have in my notes is this:
Curvature
second derivative (rate of change of tangent line)(rate of change w/ respect to arc length)
r = a smooth parameterized curve, s = arc length and T = the unit tangent vector = r'/Ir'I
curvature is κ(s) = dT/ds
then the professor got us from dT/ds to [dT/dt * 1/r'(t)] using the chain rule
so κ(s) = [dT/dt * 1/r'(t)]
Then the next class my notes have something regarding k = I a cross V I / I V I3
I am assuming that this was in regards to acceleration and velocity
I understand that curvature is the rate of change of the tangent line, but I don't know how I would approach a problem with this information if it gave me r'(t) and asked for k(t)
Thank you for your time : )
I am taking Calc III, but I am having a hard time understanding some of the concepts. Right now I am struggling with understanding the curvature of a line. What I have in my notes is this:
Curvature
second derivative (rate of change of tangent line)(rate of change w/ respect to arc length)
r = a smooth parameterized curve, s = arc length and T = the unit tangent vector = r'/Ir'I
curvature is κ(s) = dT/ds
then the professor got us from dT/ds to [dT/dt * 1/r'(t)] using the chain rule
so κ(s) = [dT/dt * 1/r'(t)]
Then the next class my notes have something regarding k = I a cross V I / I V I3
I am assuming that this was in regards to acceleration and velocity
I understand that curvature is the rate of change of the tangent line, but I don't know how I would approach a problem with this information if it gave me r'(t) and asked for k(t)
Thank you for your time : )