Section 13.2
In this worksheet we just give one example of the tangent vectors moving along a curve.
Example: Consider the curve ${\bf r}(t) = \langle t, \cos (t) \rangle$. The first animation gives the vectors ${\bf r}(t)$ as $t$ moves as red arrows. The tangent vectors are given by the green arrows.
step=0.75
P=Graphics()
v=[]
for n in srange(0,9):
P+=plot(f(t), (t,0, 2*pi));
P+=arrow((0,0),(0.1+n*step,f(0.1+n*step)),color='red')
P+=arrow((0.1+n*step,f(0.1+n*step)), (1.1+n*step, f(0.1+n*step)-sin(0.1+n*step)), color='green')
v.append(P)
a = animate(v,xmin=0)
a.show(delay = 150)
|
It may also be easier to see the tangent vectors ${\bf r'}(t)$ without the vectors ${\bf r}(t)$ as well. That is given in the following animation.
step=0.75
P=Graphics()
v=[]
for n in srange(0,9):
P+=plot(f(t), (t,0, 2*pi));
P+=arrow((0.1+n*step,f(0.1+n*step)), (1.1+n*step, f(0.1+n*step)-sin(0.1+n*step)), color='green')
v.append(P)
a = animate(v,xmin=0)
a.show(delay = 150)
|