The derivative of the unit vector is related to and vice-versa :
This may help you
Oh i thought you were saying that the two were correct.
Well, for me it's N= -bi+aj which is correct.
Derivate T.How can I make sure that N(s) is in the direction as dT/ds
As a and b are constant, we have :
According to what i wrote above :
, which is the same direction as N.
Outch, my eyes >.<
Well, if i got the pitch, T is the unit vector of V, which you can get by dividing V by its norm.
N is the normal vector of T, that is to say the derivative of T in t.
But you can also remember that if you consider a vector of (a,b) coordinates, one of its normal vector will have (b,-a) coordinates (scalar product). Another of its normal vectors will have (-a,b) coordinates. Never mind, the direction remains the same, it's just the sens that will change.
This explains the formula N=bj-ai or N=-bj+ai
Then for this :
I need more time... but it's not the thing i prefer to do :sHow can I make sure that N(s) is in the direction as dT/ds