2011-03-20, 06:04 AM
Sorry about the confusion, I tried to make the distinction by saying Vectors and Calculus instead of Vector Calculus.
I've only done dots between two vectors, and ds is just like the element of arc length, but for parametric, right?
So what I mean is, basically the book has a = a[SIZE="1"]t[/SIZE]T + a[SIZE="1"]n[/SIZE]N
If we take the square of the magnitude of a, |a|^2 = a[SIZE="1"]t[/SIZE]^2 + a[SIZE="1"]n[/SIZE]^2 and solving for a[SIZE="1"]n[/SIZE]^2 gives a[SIZE="1"]n[/SIZE] = sqrt(|a|^2 - a[SIZE="1"]t[/SIZE]^2)
And then for a[SIZE="1"]t[/SIZE], it just gives a[SIZE="1"]t[/SIZE] = d^2 s/dt^2 = d(|v|)/dt
I meant coefficients of the normal and tangential components.
I've only done dots between two vectors, and ds is just like the element of arc length, but for parametric, right?
So what I mean is, basically the book has a = a[SIZE="1"]t[/SIZE]T + a[SIZE="1"]n[/SIZE]N
If we take the square of the magnitude of a, |a|^2 = a[SIZE="1"]t[/SIZE]^2 + a[SIZE="1"]n[/SIZE]^2 and solving for a[SIZE="1"]n[/SIZE]^2 gives a[SIZE="1"]n[/SIZE] = sqrt(|a|^2 - a[SIZE="1"]t[/SIZE]^2)
And then for a[SIZE="1"]t[/SIZE], it just gives a[SIZE="1"]t[/SIZE] = d^2 s/dt^2 = d(|v|)/dt
I meant coefficients of the normal and tangential components.