python - 动画阻尼振荡器

Question

我能够在阻尼振荡下模拟质量 Spring 系统。但是，我想添加一个位置与时间的子图和另一个速度与位置(相位路径)的子图，以便我将拥有三个动画。我怎样才能添加它们？我使用的源代码如下所示
更新:我尝试添加第一个子图位置与时间的关系，但无法获得所需的曲线。

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import animation


#Constants
w = np.pi #angular frequency
b = np.pi * 0.2  #damping parameter

#Function that implements rk4 integration
def rk4(t, x, f, dt):
    dx1 = f(t, x)*dt
    dx2 = f(t+0.5*dt, x+0.5*dx1)*dt
    dx3 = f(t+0.5*dt, x+0.5*dx2)*dt
    dx4 = f(t+dt, x+dx3)*dt
    return x+dx1/6.0+dx2/3.0+dx3/3.0+dx4/6.0

#Function that returns dX/dt for the linearly damped oscillator
def dXdt(t, X):
    x = X[0]
    vx = X[1]
    ax = -2*b*vx - w**2*x
    return np.array([vx, ax])

#Initialize Variables
x0 = 5.0 #Initial x position
vx0 = 1.0 #Initial x Velocity

#Setting time array for graph visualization
dt = 0.05
N = 200
x = np.zeros(N)
vx = np.zeros(N)
y = []
# integrate equations of motion using rk4;
# X is a vector that contains the positions and velocities being integrated
X = np.array([x0, vx0])


for i in range(N):
    x[i] = X[0]
    vx[i] = X[1]
    y.append(0)
    # update the vector X to the next time step
    X = rk4(i*dt, X, dXdt, dt)

fig, (ax1, ax2) = plt.subplots(2,1, figsize=(8,6))
fig.suptitle(r' Damped Oscillation with $\beta$$\approx$' + str(round(b,2)) + r' and $\omega$$\approx$'
             + str(round(w,2)), fontsize=16)
line1, = ax1.plot([], [], lw=10,c="blue",ls="-",ms=50,marker="s",mfc="gray",fillstyle="none",mec="black",markevery=2)
line2, = ax2.plot([], [], lw=2, color='r')
time_template = '\nTime = %.1fs'
time_text = ax1.text(0.1, 0.9, '', transform=ax1.transAxes)

for ax in [ax1, ax2]:
    ax1.set_xlim(1.2*min(x), 1.2*max(x))
    ax2.set_ylim(1.2*min(x), 1.2*max(x),1)
    ax2.set_xlim(0, N*dt)
    ax1.set_yticklabels([])

def init():
    line1.set_data([], [])
    line2.set_data([], [])
    time_text.set_text('')
    return line1, line2, time_text

def animate(i):
    thisx1 = [x[i],0]
    thisy1 = [y[i],0]
    thisx2 = [i*dt,0]
    thisy2 = [x[i],0]
    line1.set_data(thisx1, thisy1)
    line2.set_data(thisx2, thisy2)
    time_text.set_text(time_template % (i*dt))
    return line1, line2, time_text  

ani = animation.FuncAnimation(fig, animate, np.arange(1, N),
                              interval=50, blit=True, init_func=init,repeat=False)

Answer 1

在对您的初始代码进行一些次要更改后，最值得注意的是:

thisx1 = [x[i],0]
thisy1 = [y[i],0]
thisx2 = [i*dt,0]
thisy2 = [x[i],0]
line1.set_data(thisx1, thisy1)
line2.set_data(thisx2, thisy2)

# should be written like this
line1.set_data([x[i],0], [y[i],0])
line2.set_data(t[:i], x[:i])
line3.set_data(x[:i], vx[:i])

工作版本，相空间图为绿色，如下所示:

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import animation


#Constants
w = np.pi #angular frequency
b = np.pi * 0.2  #damping parameter

#Function that implements rk4 integration
def rk4(t, x, f, dt):
    dx1 = f(t, x)*dt
    dx2 = f(t+0.5*dt, x+0.5*dx1)*dt
    dx3 = f(t+0.5*dt, x+0.5*dx2)*dt
    dx4 = f(t+dt, x+dx3)*dt
    return x+dx1/6.0+dx2/3.0+dx3/3.0+dx4/6.0

#Function that returns dX/dt for the linearly damped oscillator
def dXdt(t, X):
    x = X[0]
    vx = X[1]
    ax = -2*b*vx - w**2*x
    return np.array([vx, ax])

#Initialize Variables
x0 = 5.0 #Initial x position
vx0 = 1.0 #Initial x Velocity

#Setting time array for graph visualization
dt = 0.05
N = 200
t = np.linspace(0,N*dt,N,endpoint=False)
x = np.zeros(N)
vx = np.zeros(N)
y = np.zeros(N)
# integrate equations of motion using rk4;
# X is a vector that contains the positions and velocities being integrated
X = np.array([x0, vx0])

for i in range(N):
    x[i] = X[0]
    vx[i] = X[1]
    # update the vector X to the next time step
    X = rk4(i*dt, X, dXdt, dt)

fig, (ax1, ax2, ax3) = plt.subplots(3,1, figsize=(8,12))
fig.suptitle(r' Damped Oscillation with $\beta$$\approx$' + str(round(b,2)) + r' and $\omega$$\approx$'
             + str(round(w,2)), fontsize=16)
line1, = ax1.plot([], [], lw=10,c="blue",ls="-",ms=50,marker="s",mfc="gray",fillstyle="none",mec="black",markevery=2)
line2, = ax2.plot([], [], lw=1, color='r')
line3, = ax3.plot([], [], lw=1, color='g')
time_template = '\nTime = %.1fs'
time_text = ax1.text(0.1, 0.9, '', transform=ax1.transAxes)


ax1.set_xlim(1.2*min(x), 1.2*max(x))
ax1.set_xlabel('x')
ax1.set_ylabel('y')

ax2.set_ylim(1.2*min(x), 1.2*max(x),1)
ax2.set_xlim(0, N*dt)
ax2.set_xlabel('t')
ax2.set_ylabel('x')

ax3.set_xlim(1.2*min(x), 1.2*max(x),1)
ax3.set_ylim(1.2*min(vx), 1.2*max(vx),1)
ax3.set_xlabel('x')
ax3.set_ylabel('vx')

def init():
    line1.set_data([], [])
    line2.set_data([], [])
    line3.set_data([], [])
    time_text.set_text('')
    return line1, line2, line3, time_text

def animate(i):
    line1.set_data([x[i],0], [y[i],0])
    line2.set_data(t[:i], x[:i])
    line3.set_data(x[:i], vx[:i])
    time_text.set_text(time_template % (i*dt))
    return line1, line2, line3, time_text  

ani = animation.FuncAnimation(fig, animate, np.arange(1, N),
                              interval=50, blit=True, init_func=init,repeat=False)

ani.save('anim.gif')

并给出: