Re: help about klotoid-integral-solution
- To: mathgroup@smc.vnet.net
- Subject: [mg12546] Re: [mg12502] help about klotoid-integral-solution
- From: Alfred Gray <gray@hypatia.umd.edu>
- Date: Sat, 23 May 1998 18:11:09 -0400
You can find Mathematica programs for the clothoid and its generalizations in my book, listed below. The programs are available via anonymous ftp from bianchi.umd.edu. The most straightforward definition of the clothoid uses Mathematica's FresnelS and FresnelC, but then it plots very slowly. A definition of the clothoid using NDSolve plots much faster. Alfred Gray %%%%%%%%%%%%%%%%%%%%%%%%%% Visit the galleries of surfaces and curves: http://bianchi.umd.edu Just published: Modern Differential Geometry of Curves and Surfaces, Second Edition. CRC Press, December 1997. On Tue, 19 May 1998, eckhard_FABIAN wrote: > 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. > >