Python 仿真问题：系数随机变化的 ODE 系统

Question

I'm pretty new to this type of problem, so I appreciaty any help.

I'm trying to simulate a dipole-dipole interaction problem, where one large dipole is stationary at the origin and another (small dipole) is located somewhere inside the electric field of the larger one. I'm trying to find the path the smaller dipole takes given some orientation and starting position.

The catch is that the orientation of the small dipole randomly changes at every time step. I have managed to simulate this problem if the orientation of the small dipole is kept constant using scipy.integrate.odeint

When I try to solve the same problem, but with the dipole orienation changing randomly, i get the following error:

ODEintWarning: Excess work done on this call (perhaps wrong Dfun type). Run with full_output = 1 to get quantitative information.
warnings.warn(warning_msg, ODEintWarning)

Can I fix this? Should I use another method of numerical integration that is better suited for this, and if so which one?

Here is the relevant part of my code

from cmath import exp
from scipy.integrate import odeint 
import numpy as np

#constants
pv = 10e12
m = 1
Q = 6.95e-12
K = pv*(1/m)*Q



def px(t):
  return np.random.normal()

def py(t):
  return np.random.normal()

def pz(t):
  return np.random.normal()



def odes(q,t, px, py, pz): #q is a vector


  #u1 = x, v1 = y, w1 = z, ...
  u1 = q[0]
  v1 = q[1]
  w1 = q[2]
  u2 = q[3]
  v2 = q[4]
  w2 = q[5]

  du1dt = u2
  dv1dt = v2
  dw1dt = w2

  #Force
  du2dt = (u1**2 + v1**2 + w1**2)**(-2.5)*(px(t)*(-2*u1 + w1**2 + v1**2)*w1 - py(t)*3*u1*v1*w1 + pz(t)*(-2*w1**2 + u1**2 + v1**2)*u1)
  dv2dt = (u1**2 + v1**2 + w1**2)**(-2.5)*(-px(t)*3*u1*v1*w1 + py(t)*(-2*v1**2 + w1**2 + u1**2) + pz(t)*(-2*w1**2 + u1**2 + v1**2)*v1) 
  dw2dt = (u1**2 + v1**2 + w1**2)**(-2.5)*(-px(t)*3*(w1**2 - pv)*u1 - py(t)*3*(w1**2 - pv)*v1 + pz(t)*(3*pv + 2*u1**2 + 2*v1**2 - w1**2)*w1)

  return [du1dt, dv1dt, dw1dt, du2dt, dv2dt, dw2dt]

#initial conditions
x0 = 90
y0 = 110
z0 = 100

dxdt0 = 0
dydt0 = 0
dzdt0 = 0
q0 = [x0, y0, z0, dxdt0, dydt0, dzdt0]


T = 10
dt = 0.0025
t = np.linspace(0, T, int(T//dt))


args = (px,py,pz)
q = odeint(odes, q0, t, args)

x = q[:,0]
y = q[:,1]
z = q[:,2]