Originally Posted by
topsquark Any unit vector parallel to the yz plane will take the form:
<0, cos(phi), sin(phi)>
So r(t) must be proportional to one of these in general.
Comparing the x components we see that
cos(t^2) = 0
Thus
t^2 = (2n + 1)pi/2 for n = 0, 1, 2, ...
t = (+/-)sqrt{(2n + 1)pi/2}
Additionally, dividing the z component by the y component gives us:
e^(sqrt(t))/t = tan(phi)
Since tan(phi) can be any angle t can be any value, so this doesn't give any restrictions on t. So the solution is:
t = (+/-)sqrt{(2n + 1)pi/2}
-Dan