Warum dauert meine 3D -Doppelpendelsimulation zu lange? ⇐ Python

[Anonymous]

Ich versuche, ein 3D -Doppelpendel mit Python, Sympy und Scipy zu simulieren. Ziel ist es, die LaGrange -Gleichungen zu lösen und die Ergebnisse zu belasten. Das Skript wird jedoch auf unbestimmte Zeit ausgeführt, und ich habe über 30 Minuten gewartet, ohne eine Ausgabe zu sehen. Gleichungen. Hier ist mein relevanter Code: < /p>

Code: Select all

import numpy as np
import sympy as smp
from scipy.integrate import odeint
import matplotlib.pyplot as plt
from matplotlib import animation
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import PillowWriter

t, g = smp.symbols("t g")
m1, m2 = smp.symbols("m1 m2")
L1, L2 = smp.symbols("L1 L2")

the1, the2, phi1, phi2 = smp.symbols(r"\theta_1 \theta_2 \phi_1 \phi_2", cls=smp.Function)
the1 = the1(t)
the2 = the2(t)
phi1 = phi1(t)
phi2 = phi2(t)

the1_d = smp.diff(the1, t)
the2_d = smp.diff(the2, t)
phi1_d = smp.diff(phi1, t)
phi2_d = smp.diff(phi2, t)
the1_dd = smp.diff(the1_d, t)
the2_dd = smp.diff(the2_d, t)
phi1_dd = smp.diff(phi1_d, t)
phi2_dd = smp.diff(phi2_d, t)

x1 = L1*smp.sin(the1)*smp.cos(phi1)
y1 = L1*smp.sin(the1)*smp.sin(phi1)
z1 = -L1*smp.cos(the1)
x2 = x1 + L2*smp.sin(the2)*smp.cos(phi2)
y2 = y1 + L2*smp.sin(the2)*smp.sin(phi2)
z2 = z1 -L2*smp.cos(the2)

# Kinetic
T1 = smp.Rational(1,2) * m1 * (smp.diff(x1, t)**2 + smp.diff(y1, t)**2 + smp.diff(z1, t)**2)
T2 = smp.Rational(1,2) * m2 * (smp.diff(x2, t)**2 + smp.diff(y2, t)**2 + smp.diff(z2, t)**2)
T = T1+T2
# Potential
V1 = m1*g*z1
V2 = m2*g*z2
V = V1 + V2
# Lagrangian
L = T-V

LE1 = (smp.diff(L, the1) - smp.diff(smp.diff(L, the1_d), t)).simplify()
LE2 = (smp.diff(L, the2) - smp.diff(smp.diff(L, the2_d), t)).simplify()
LE3 = (smp.diff(L, phi1) - smp.diff(smp.diff(L, phi1_d), t)).simplify()
LE4 = (smp.diff(L, phi2) - smp.diff(smp.diff(L, phi2_d), t)).simplify()

sols = smp.solve([LE1, LE2, LE3, LE4], (the1_dd, the2_dd, phi1_dd, phi2_dd),
simplify=False, rational=False)

do1dt_f = smp.lambdify((t,g,m1,m2,L1,L2,the1,the2,the1_d,the2_d,phi1,phi2,phi1_d,phi2_d), sols[the1_dd])
do2dt_f = smp.lambdify((t,g,m1,m2,L1,L2,the1,the2,the1_d,the2_d,phi1,phi2,phi1_d,phi2_d), sols[the2_dd])
dthe1dt_f = smp.lambdify(the1_d, the1_d)
dthe2dt_f = smp.lambdify(the2_d, the2_d)

dw1dt_f = smp.lambdify((t,g,m1,m2,L1,L2,the1,the2,the1_d,the2_d,phi1,phi2,phi1_d,phi2_d), sols[phi1_dd])
dw2dt_f = smp.lambdify((t,g,m1,m2,L1,L2,the1,the2,the1_d,the2_d,phi1,phi2,phi1_d,phi2_d), sols[phi2_dd])
dphi1dt_f = smp.lambdify(phi1_d, phi1_d)
dphi2dt_f = smp.lambdify(phi2_d, phi2_d)

def dSdt(S, t, g, m1, m2, L1, L2):
the1, the2, phi1, phi2, o1, o2, w1, w2 = S
return [
dthe1dt_f(o1),
dthe2dt_f(o2),
dphi1dt_f(w1),
dphi2dt_f(w2),
do1dt_f(t, g, m1, m2, L1, L2, the1, the2, o1, o2, phi1, phi2, w1, w2),
do2dt_f(t, g, m1, m2, L1, L2, the1, the2, o1, o2, phi1, phi2, w1, w2),
dw1dt_f(t, g, m1, m2, L1, L2, the1, the2, o1, o2, phi1, phi2, w1, w2),
dw2dt_f(t, g, m1, m2, L1, L2, the1, the2, o1, o2, phi1, phi2, w1, w2),
]

t = np.linspace(0, 20, 100)
g = 9.81
m1=2
m2=1
L1 = 2
L2 = 1
ans = odeint(dSdt, y0=[np.pi/3, np.pi/3, 0, -np.pi, 3, 10, -2, -10], t=t,     args=(g,m1,m2,L1,L2))

def get_pos(the1, the2, phi1, phi2, L1, L2):
return (L1*np.sin(the1)*np.cos(phi1),
L1*np.sin(the1)*np.sin(phi1),
-L1*np.cos(the1),
L1*np.sin(the1)*np.cos(phi1)+L2*np.sin(the2)*np.cos(phi2),
L1*np.sin(the1)*np.sin(phi1)+L2*np.sin(the2)*np.sin(phi2),
-L1*np.cos(the1)-L2*np.cos(the2))

x1, y1, z1, x2, y2, z2 = get_pos(ans.T[0], ans.T[1], ans.T[2], ans.T[3], L1, L2)

def animate(i):
ln1.set_data([0, x1[i], x2[i]], [0, y1[i], y2[i]])
ln1.set_3d_properties([0, z1[i], z2[i]])

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.set_facecolor("k")
ax.set_xticks([])
ax.set_yticks([])
ax.set_zticks([])
ax.set_xlim(-4, 4)
ax.set_ylim(-4, 4)
ax.set_zlim(-4, 4)
ln1, = ax.plot([], [], [], 'ro--', lw=3, markersize=8)
ani = animation.FuncAnimation(fig, animate, frames=1000, interval=50)
ani.save('pen2.gif',writer='pillow',fps=25)

Danke für Empfehlungen.