#Fourth-Order Forest Ruth
for j in range(len(dt)):
r_0 = [(1, 0, 0)]
v_0 = [(0, .5, 0)]
t = 0
r = r_0
v = v_0
s = 2**(1 / 3)
H = dt[j] / (2 - s)
for i in range(0, int((6 * np.pi) / dt[j])):
v_n = np.asarray(v[len(v) - 1])
r_n = np.asarray(r[len(r) - 1])
r_n = use.int_q_array(r_n, v_n, .5 * dt[j])
B = np.asarray([0, 0, 1 / (r_n[0]**2)])
v_n = use.v_magnetic_calc(r_n, v_n, B, dt[j])
r_n = use.int_q_array(r_n, v_n, .5 * dt[j])
r.append(r_n)
v.append(v_n)
r = np.asarray(r)
x_val = [x[0] for x in r]
y_val = [x[1] for x in r]
ax3.plot(x_val, y_val)
###################################################
###################################################
#graphing
# y_0 = -50
# v_int = 1/10
# r_0 = [(x_0, 0)]
# v_0 = [(0, v_int)]
# r = r_0
# v = v_0
# A_x = []
# A_y = []
for i in range(0, int(10000)):
v_n = np.asarray(v[len(v) - 1])
r_n = np.asarray(r[len(r) - 1])
r_n = use.int_q_array(r_n, v_n, .5 * t)
v_n = use.int_v_array(r_n, r1, r2, v_n, t)
r_n = use.int_q_array(r_n, v_n, .5 * t)
# if i > 9991:
# print(r)
# exit()
# print('we made it through!!')
r.append(r_n)
v.append(v_n)
r = np.asarray(r)
l = []
x_val = [x[0] for x in r]
y_val = [x[1] for x in r]
for j in range(len(dt)):
r_0 = [(1, 0, 0)]
v_0 = [(0, .5, 0)]
t = 0
r = r_0
v = v_0
s = 2**(1 / 3)
H = dt[j] / (2 - s)
for i in range(0, int((6 * np.pi) / dt[j])):
v_n = np.asarray(v[len(v) - 1])
r_n = np.asarray(r[len(r) - 1])
#############
r_n = use.int_q_array(r_n, v_n, .5 * H)
B = np.asarray([0, 0, 1 / r_n[0]**2])
v_n = use.v_magnetic_calc(r_n, v_n, B, H)
r_n = use.int_q_array(r_n, v_n, .5 * H)
##############
r_n = use.int_q_array(r_n, v_n, -.5 * s * H)
B = np.asarray([0, 0, 1 / r_n[0]**2])
v_n = use.v_magnetic_calc(r_n, v_n, B, -s * H)
r_n = use.int_q_array(r_n, v_n, -.5 * s * H)
#############
r_n = use.int_q_array(r_n, v_n, .5 * H)
B = np.asarray([0, 0, 1 / r_n[0]**2])
v_n = use.v_magnetic_calc(r_n, v_n, B, H)
r_n = use.int_q_array(r_n, v_n, .5 * H)
##############
r.append(r_n)