/*--- leap: takes a leapfrog step ---*/
double leap(CHAIN * C, double h)
{
double dTdP[C->N-1][3], dUdQ[C->N-1][3], du1[C->N-1][3], du2[C->N-1][3], T, a1, a0, U, Pt = -(C->E);
//set up to calculate Q_1/2
T = calc_T(C);
a0 = 1/(2.0*(T + Pt));
calc_dT(C,dTdP);
mat_scalar_mult(C->N-1,3,dTdP,h*a0,dTdP); //multiplied dTdP by scalar a
mat_add(C->N-1,3,C->R,dTdP,C->R); //this has updated C->R to equal Q_1/2
//calculate P_1
calc_dU1(C,du1);
calc_dU2(C,du2);
mat_add(C->N-1,3,du1,du2,dUdQ);
U = calc_U(C);
mat_scalar_mult(C->N-1,3,dUdQ, -h/U ,dUdQ); //multiplied dUdQ by scalar -h/U
mat_add(C->N-1,3,C->W,dUdQ,C->W); //this has updated C->W to equal P_1
//set up to calculate Q_1
T = calc_T(C);
a1 = 1/(2.0*(T + Pt));
calc_dT(C,dTdP);
mat_scalar_mult(C->N-1,3,dTdP,h*a1,dTdP); //multiplied dTdP by scalar a
mat_add(C->N-1,3,C->R,dTdP,C->R); //this has updated C->R to equal Q_1/2
return h/2.0 * (a1 + a0); //returns update for time value, so use t += leap(C,h);
}
double calc_time_derivs(double *de, double *x, double *y, double *gamma,
double c[],
double *vx, double *vy, double *dgamma, int np) {
int j;
double *xe, *ye, *se, *kappa, *dgamma_pre, *T, *U, *wx, *wy;
xe = vector(np);
ye = vector(np);
se = vector(np);
kappa = vector(np);
dgamma_pre = vector(np);
T = vector(np);
U = vector(np);
wx = vector(np);
wy = vector(np);
d1(x, de, 1.0, np, xe);
d1(y, de, 0.0, np, ye);
for(j = 0; j < np; j++)
se[j] = sqrt(xe[j]*xe[j] + ye[j]*ye[j]);
calc_curvature(de, x, y, xe, ye, se, np, kappa);
birkhoff_integral(de, x, y, xe, ye, se, gamma, c[3], np, wx, wy);
printf("\nU:\n");
for(j = 0; j < np; j++) {
U[j] = (-ye[j]*wx[j] + xe[j]*wy[j])/se[j];
printf("%i: %e\n", j, U[j]);
}
calc_T(de, xe, ye, U, np, T);
for(j = 0; j < np; j++) {
dgamma_pre[j] =
+ (T[j] - (wx[j]*xe[j]+wy[j]*ye[j])/se[j])*gamma[j]/se[j]
+ c[0]*kappa[j]
- c[1]*U[j]
- c[2]*y[j];
vx[j] = (-ye[j]*U[j] + xe[j]*T[j])/se[j];
vy[j] = ( xe[j]*U[j] + ye[j]*T[j])/se[j];
}
d1(dgamma_pre, de, 0.0, np, dgamma);
free(xe);
free(ye);
free(se);
free(kappa);
free(dgamma_pre);
free(T);
free(U);
free(wx);
free(wy);
return 0.0;
}
matrix calc_H(int l, double R, double M)
{
matrix H = matrix_add(calc_V(l, R), calc_T(l, M, R));
return H;
}
