help about klotoid-integral-solution
- To: mathgroup@smc.vnet.net
- Subject: [mg12502] help about klotoid-integral-solution
- From: fabian@kdt.de (eckhard_FABIAN)
- Date: Tue, 19 May 1998 13:32:03 -0400
- Organization: The Math Forum
it would be great if anyone can help with the solution of the integrals
for x and y of the klothoid: x=a*sqrt(pi)*INT(cos(pi*u*u/2)du,u=0...t)
y=a*sqrt(pi)*INT(sin(pi*u*u/2)du,u=0...t) with t=s/(a*sqrt(pi))
s=OM Distance on the curve from origin O to point M on the curve
and a>0
The point O is the centre of symmetry of the curve, it has the
asymptotic points
A(a*sqrt(pi)/2,a*sqrt(pi)/2) and B(-a*sqrt(pi)/2,-a*sqrt(pi)/2) These
formula are ref. in the book
BRONSTEIN/SEMENDJAJEW TASCHENBUCH DER MATHEMATIK I need formula to
calculate the x and y -coordinates depending on the increasing distance
on the curve. Thanks a lot for an answer via email.