// SR universe. Natural units
// How long to rotate (through a finite angle) a 2D cylinder of radius 1
// The whole thing is done in polar coordinates
// Usage: caseP nnn where nnn is a percentage of a full rotation
#include <stdio.h>
#include <math.h>
#define INTERVAL 0.001 // time increment
#define PI 3.14159265 // Full turn
int main(int ac, char **av)
{
double gammI, // lorentz factor (inverted)
speedT, speedR, // speed tangential, radial
posT = 0, posR = 1, // position tangential (radians), radial
time = 0,
vt, vr, dt, goal; // vel, delta tangent pos
int ix = 0, percent = 25; // default
if (ac > 1) { // If percent arg supplied
char *p = *++av;
percent = 0;
while (*p >= '0' && *p <= '9')
percent = percent * 10 + *p++ - '0';
}
goal = (PI * (double)percent) / 100.;
while (1) {
gammI = posR; // 1st estimate
vt = sqrt(1 - gammI * gammI); // v from contraction
vr = sqrt(1 - vt * vt); // vel inward
gammI = posR - vr * INTERVAL / 2; // mid-interval radius / gammI
vt = sqrt(1 - gammI * gammI); // 2nd estimate, average v
vr = sqrt(1 - vt * vt); // avg vel inward
dt = (INTERVAL * vt) / gammI; // delta radians
if (posT + dt > goal) break;
posT += dt;
posR -= INTERVAL * vr;
// printf("G%f t%f r%f T%f R%f\n", gammI, vt, vr, posT, posR); // debug
time += INTERVAL;
}
double frac = (goal - posT) / dt;
time += INTERVAL * frac;
posR += INTERVAL * vr * frac;
printf("time %f, min radius %f\n", time * 2, posR); // *2 for return trip
return 0;
}
