Hello
If I have an unit vector the derivative is an orthogonal vector (orthogonality is enough easy to demonstrate)
How I can demonstrate that the derivative of unit vector is not an unit vectors ?
Thanks !
perfect !
Can I demonstrate in this way?
the versor
$\displaystyle \hat{v}(t) = \cos(\theta(t))\hat{i} + \sin(\theta(t))\hat{j}$
and its derivative
$\displaystyle \hat{v}'(t) = \theta'(t)(-\sin(\theta(t))\hat{i} + \cos(\theta(t))\hat{j})$
where :
$\displaystyle (-\sin(\theta(t))\hat{i} + \cos(\theta(t))\hat{j})$
is the orthogonal versor
and theta(t)
$\displaystyle \theta'(t)$
in general different to 1 ?