Mathc initiation/a45
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c00c2.c |
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/* --------------------------------- */
/* save as c00c2.c */
/* --------------------------------- */
#include "x_hfile.h"
#include "fc.h"
/* --------------------------------- */
int main(void)
{
double x = 2.;
clrscrn();
printf(" If a smooth curve C is the graph of y = f(x), \n"
" then the curvature K at P(x,y) is\n\n\n"
" K = |y''| / [1 + y'^2]^(3/2) \n\n\n"
" If P(x,y) is a point on the graph of y = f(x) \n"
" at which K != 0. The point M(h,k) is the center\n"
" of the cuvature for P if \n\n\n"
" h = x - y'[1 + y'^2] / y'' \n"
" k = y + [1 + y'^2] / y'' \n\n\n"
" The radius is r = 1/K \n\n\n");
stop();
clrscrn();
printf(" Find the curvature K of the curve at P(%+.2f,%+.2f) with\n\n\n",
x,f(x));
printf(" K = |y''| / [1 + y'^2]^(3/2) \n\n\n");
printf(" f : x-> %s \n\n\n", feq);
printf(" At the point P(%+.2f,%+.2f) K = %+.2f\n\n\n",
x,f(x),K_y_2d(f,x));
stop();
clrscrn();
printf(" Find the centre of the cuvature M(h,k)\n\n");
printf(" h = x - y'[1 + y'^2] / y'' \n");
printf(" k = y + [1 + y'^2] / y'' \n\n\n");
printf(" for the point P(%+.2f,%+.2f) with\n\n", x,f(x));
printf(" f : x-> %s \n\n\n", feq);
printf(" At the point P(%+.2f,%+.2f)\n\n",x,f(x));
printf(" The centre of the cuvature is M(%+.2f,%+.2f)\n\n\n",
h_y_2d(f,x),
k_y_2d(f,x) );
stop();
return 0;
}
/* --------------------------------- */
/* --------------------------------- */
Exemple de sortie écran :
Find the curvature K of the curve at P(+2.00,+0.00) with
K = |y''| / [1 + y'^2]^(3/2)
f : x-> log(x-1)
At the point P(+2.00,+0.00) K = +0.35
Press return to continue.
Find the centre of the cuvature M(h,k)
h = x - y'[1 + y'^2] / y''
k = y + [1 + y'^2] / y''
for the point P(+2.00,+0.00) with
f : x-> log(x-1)
At the point P(+2.00,+0.00)
The centre of the cuvature is M(+4.00,-2.00)
Press return to continue.