Scipy ode根据解的大小积分到t的未知极限 [英] Scipy ode integrate to unknown limit of t, based on the size of solution

问题描述

我正在模拟在电磁场中移动的带电粒子，并且正在使用scipy ode.显然，此处的代码已简化，但仅作为示例.我的问题是我想在限制r而不是t之后结束积分.因此，将dx/dt积分到norm(x)> r.

I am modeling charged particles moving through an electromagnetic field and am using scipy ode. The code here is simplified, obviously, but works as an example. The problem I have is that I want to end the integration after a limit on r, not on t. So, integrate dx/dt up to the point where norm(x) > r.

但是，我不想仅更改函数以在r上积分，因为位置是t的函数.我可以对不相关的变量或某些东西进行定积分吗?

I don't want to just change the function to integrate over r, however, because the position is a function of t. Can I do a definite integral over an unrelated variable or something?

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint

def RHS(state, t, Efield, q, mp):

    ds0 = state[3]
    ds1 = state[4]
    ds2 = state[5]
    ds3 = q/mp * Efield*state[0]
    ds4 = q/mp * Efield*state[1]
    ds5 = q/mp * Efield*state[2]

    r = np.linalg.norm((state[0], state[1], state[2]))

    # if r > 30000 then do stop integration.....?

    # return the two state derivatives
    return [ds0, ds1, ds2, ds3, ds4, ds5]


ts = np.arange(0.0, 10.0, 0.1)
state0 = [1.0, 2.0, 3.0, 0.0, 0.0, 0.0]

Efield=1.0
q=1.0
mp=1.0

stateFinal = odeint(RHS, state0, ts, args=(Efield, q, mp))
print(np.linalg.norm(stateFinal[-1,0:2]))

推荐答案

您可以使用请注意，对于ode，必须将RHS的签名更改为def RHS(t, state, Efield, q, mp):，与odeint不同，自变量是最先出现的.

Note that the signature of RHS will have to be changed to def RHS(t, state, Efield, q, mp): for ode, the independent variable comes first, unlike in odeint.

输出是以自变量dt的增量计算的解，直到循环结束为止(因为达到t_max或积分器失败，或者遇到了break的条件) ).

The output is the solution computed in the increments of dt of independent variable, up to the time when the loop ends (either because t_max is reached, or integrator fails, or the condition for break was encountered).

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