I'm learning about reparametrizing curves and I don't understand what my teacher did in the following example :
Reparametrize the helix from in the same direction than increases.
Then she continues from this and I understand all she did.
What I don't understand is why the lower bound of the integral is 0.
It's sometimes different from 0, so how do I know what lower bound to chose? I'm sure it's because of the (1,0,0) point, but why 0 as lower bound? Is it because the z-coordinate is worth 0 in (1,0,0)?
April 4th 2009, 12:24 AM
You are reparameterizing in terms of arc length so s(t) is the distance traveled in time t.
In most instances you are at the initial point when t= 0 which is why the bottom limit is 0. you are at the point (1,0,0) at t = 0. It has nothing to do with the spatial coordinates but rather the time coordinate.
If for instance you were at the initial point (1,0,0) at t= t0 then t0 would be the lower limit of integration