限制ODEINT Python的输出

Question

我正在尝试为Scipy的odeint函数的返回值定义“硬”限制，但我不确定函数是否允许这样做。我已经从Scipy Cookbook修改了这个例子，以便耦合的两个体系可能会发生碰撞。

图片链接

图表冲突

虚构停止

具体而言，弹簧常数和质量已经变得更弱更轻。您还会注意到函数内部使用的'if'语句试图限制'm1'的行程，而不是'x2'的初始输入。对不起，我没有足够的声望点来发布图表，但你会清楚地看到两个质量可以在部分解决方案中占据相同的空间。

# Use ODEINT to solve the differential equations defined by the vector field
from scipy.integrate import odeint
import matplotlib.pyplot as plt
import numpy as np

def vectorfield(w, t, p):
"""
Defines the differential equations for the coupled spring-mass system.

Arguments:
    w :  vector of the state variables:
              w = [x1,y1,x2,y2]
    t :  time
    p :  vector of the parameters:
              p = [m1,m2,k1,k2,L1,L2,b1,b2]
"""
x1, y1, x2, y2 = w
m1, m2, k1, k2, L1, L2, b1, b2 = p

# Create f = (x1',y1',x2',y2'):
f = [y1,
     (-b1 * y1 - k1 * (x1 - L1) + k2 * (x2 - x1 - L2)) / m1,
     y2,
     (-b2 * y2 - k2 * (x2 - x1 - L2)) / m2]

if y1 > x2:
    y1 == x2
else:
    y1 == y1

return f


# Parameter values
# Masses:
m1 = 0.5
m2 = 1.5
# Spring constants
k1 = 0.1
k2 = 40.0
# Natural lengths
L1 = 0.5
L2 = 1.0
# Friction coefficients
b1 = 0.8
b2 = 0.5

# Initial conditions
# x1 and x2 are the initial displacements; y1 and y2 are the initial velocities
x1 = 0.5
y1 = 0.0
x2 = 4.25
y2 = 0.0

# ODE solver parameters
abserr = 1.0e-8
relerr = 1.0e-6
stoptime = 5.0
numpoints = 2500

# Create the time samples for the output of the ODE solver.
# I use a large number of points, only because I want to make
# a plot of the solution that looks nice.
t = [stoptime * float(i) / (numpoints - 1) for i in range(numpoints)]

# Pack up the parameters and initial conditions:
p = [m1, m2, k1, k2, L1, L2, b1, b2]
w0 = [x1, y1, x2, y2]

# Call the ODE solver.
wsol = odeint(vectorfield, w0, t, args=(p,),
              atol=abserr, rtol=relerr)

plt.plot(t, wsol[:, 0], 'b', label='theta(t)')
plt.plot(t, wsol[:, 2], 'g', label='omega(t)')
plt.show()

我不确定我的变量是否设置不正确，或者odeint函数是否不能接受我试图添加的这些类型的“限制”。理想情况下，如果可以设置“上边界”，如果质量的位移超过该值，则可以将其设置为等于最大排序限制。

提前感谢您的帮助。