|
|
Hi Bob,
This is is far from blindingly obvious! I hope i didn't make a mistake
though...
the parameterized path function should be:
f(t)=[x(t),y(t),z(t)]=[H*t,(r+(R-r)*t)*sin(2*pi*n*t),(r+(R-r)*t)*cos(2*pi*n*t)]
where t goes from 0 (bottom y=0, r) to 1 (top y=H, R).
if you continue from here the results are getting pretty ugly (tbh i'm
surprised they are getting *that* ugly) but anyway: the total length of the
path is:
a) L = (H^2 + (r - R)^2)*LN((sqrt(H^2 + (2*pi*n*r)^2 + (r - R)^2) -
2*pi*n*r)/(sqrt(H^2 + (2*pi*n*R)^2 + (r - R)^2) - 2*pi*n*R))/(4*pi*n*(R -
r)) + r*sqrt(H^2 + (2*pi*n*r)^2 + (r - R)^2)/(2*(r - R)) + R*sqrt(H^2 +
(2*pi*n*R)^2 + (r - R)^2)/(2*(R - r))
where x^2 is pow(x,2) (and no i didn't calculate this by hand ;-))
I couldn't solve b) and i doubt it would be any nicer than a)
Does this help? :-)
Regards Roman
Post a reply to this message
|
|