1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
| import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation
from matplotlib.widgets import Button
##############################################################################
# Initialisation de pyplot
##############################################################################
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.view_init(azim=45, elev=27)
ax.set_xlim(-2, 2)
ax.set_ylim(-2, 2)
ax.set_zlim(-2, 2)
ax.set_aspect('equal')
x, y, z = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
ax.plot([0, 1], [0, 0], [0, 0], linestyle='dashed', color='k')
ax.plot([0, 0], [0, 1], [0, 0], linestyle='dashed', color='k')
ax.plot([0, 0], [0, 0], [0, 1], linestyle='dashed', color='k')
u, v, w = 0.5*np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
ax.quiver(x, y, z, u, v, w, color='k')
ax.text(1.8, 0, 0, r'$x$', color='k')
ax.text(0, 1.6, 0, r'$y$', color='k')
ax.text(0, 0, 1.6, r'$z$', color='k')
# Oxy
theta = np.linspace(-1, 3*np.pi/4, 100)
phi = np.linspace(0, np.pi, 100)
x = np.sin(theta)
y = np.cos(theta)
z = np.zeros(len(theta))
ax.plot(x, y, z, color='k')
# Ozx
theta = np.linspace(-1, 3*np.pi/4, 100)
phi = np.linspace(0, np.pi, 100)
x = np.zeros(len(theta))
y = np.sin(theta)
z = np.cos(theta)
ax.plot(x, y, z, color='k')
# Ozy
theta = np.linspace(-1, 3*np.pi/4, 100)
phi = np.linspace(0, np.pi, 100)
x = np.sin(theta)
y = np.zeros(len(theta))
z = np.cos(theta)
ax.plot(x, y, z, color='k')
# Dessin du vecteur moment cinétique
#LO = [np.random.normal(0, 1) for i in range(3)]
LO = np.array([1, 3, 3])
LO = LO / np.sqrt(np.sum(c**2 for c in LO))
LO_hist = np.array([LO])
LO_line = ax.quiver(0, 0, 0, *LO, color='b')
LO_shad = ax.quiver(0, 0, 0, LO[0], LO[1], 0, color='grey')
LO_text = ax.text(*LO, r'$L_O$', color='b')
LO_pers, = ax.plot([], [], [], color='b')
# Dessin du vecteur champ B0
B0_base = np.array([0, 0, 2])
B0 = np.array([0, 0, 1])
B0_line = ax.quiver(*B0_base, *B0, color='r')
B0_text = ax.text(*(B0_base + B0), r'$B_0$', color='red')
# Dessin du vecteur champ B1
B1 = np.array([0, 0, 0])
B1_line = ax.quiver(*B0_base, *B1, color='r')
B1_text = ax.text(*(B0_base + B1), r'$b_1$', color='r')
B1_pers, = ax.plot([], [], [], color='r')
wB1 = 1
B1_cooldown = 0
##############################################################################
# Fonction pour pivoter un vecteur
##############################################################################
def rotate_vec(V, w, axe, hist=None):
if hist is not None:
if len(hist) > 200:
hist = np.delete(hist, 0, axis=0)
hist = np.append(hist, [V], axis=0)
else:
hist = []
# Le vecteur autour duquel tourner doit être unitaire
x, y, z = axe / np.sqrt(np.sum(c**2 for c in axe))
# Angle de rotation
a = w * dt
# Matrice de rotation
c = np.cos(a)
s = np.sin(a)
t = 1-c
R = np.array([
[t*x*x+c, t*x*y-s*z, t*x*z+s*y],
[t*x*y+s*z, t*y*y+c, t*y*z-s*x],
[t*x*z-s*y, t*y*z+s*x, t*z*z+c]])
# Calcul du nouveau vecteur
V = np.matmul(V, R)
return V, hist
dt = 1e-1
##############################################################################
# Fonction pour avancer de dt
##############################################################################
def step():
#####################################################
# Mise à jour de B1 (rotation)
global B1, B1_cooldown
B1_cooldown -= dt
if B1_cooldown > 0:
if np.array_equal(B1, np.array([0, 0, 0])):
B1 = np.array([0, 1e-1, 0])
else:
B1, B1_hist = rotate_vec(B1, wB1, [0, 0, 1])
else:
B1_cooldown = 0
B1 = np.array([0, 0, 0])
#####################################################
# Mise à jour de LO (rotation)
global LO, LO_hist
# Champ total
B = B0 + B1
# Vitesse de rotation
w = np.sqrt(np.sum(c**2 for c in B)) * np.sqrt(np.sum(c**2 for c in LO))
LO, LO_hist = rotate_vec(LO, w, B, LO_hist)
# Mise à jour de LO (relaxation)
w = (LO[2] - 1) / 100
v = LO - LO_hist[-1]
LO, LO_hist = rotate_vec(LO, w, v, LO_hist)
##############################################################################
# Bouttons
##############################################################################
def relax_LO():
global LO
LO = np.array([0.001, 0.001, 1])
LO = LO / np.sqrt(np.sum(c**2 for c in LO))
def activate_b1(cooldown):
global B1_cooldown
B1_cooldown = cooldown
relax = Button(plt.axes([0.9, 0, 0.1, 0.1]), 'relax')
relax.on_clicked(lambda x: relax_LO())
demo = Button(plt.axes([0, 0, 0.1, 0.1]), 'b1, demo')
demo.on_clicked(lambda x, CD=0.26*np.pi/(2*wB1)/dt: activate_b1(CD))
perfect = Button(plt.axes([0.2, 0, 0.1, 0.1]), 'b1, rmn')
perfect.on_clicked(lambda x, CD=np.pi/(2*wB1)/dt: activate_b1(CD))
##############################################################################
# Affichage
##############################################################################
def animate(i):
fig.suptitle("t = {:2.4f} \n b1: {:2.4f}".format(i*dt, B1_cooldown))
step()
global B1_line, B1_shad, B1_text
B1_line.remove()
B1_text.remove()
B1_line = ax.quiver(*B0_base, *(B1*5), color='r')
B1_text = ax.text(*(B0_base + B1), r'$b_1$', color='r')
global LO_line, LO_shad, LO_text
LO_line.remove()
LO_shad.remove()
LO_text.remove()
LO_line = ax.quiver(0, 0, 0, *LO, color='b')
LO_shad = ax.quiver(0, 0, 0, LO[0], LO[1], 0, color='grey')
LO_text = ax.text(*LO, r'$L_0$', color='b')
LO_pers.set_data(LO_hist[:, 0], LO_hist[:, 1])
LO_pers.set_3d_properties(LO_hist[:, 2])
dt_anim = int(np.round(dt*1e3) + 0.1)
anim = FuncAnimation(fig, animate, interval=1)
plt.show()
|