Question

我试图用Euler和Range-Kutta方法解决弹簧质量问题并比较这些图。我已经为Euler和Runge-Kutta编写了函数，但在调用函数解决了我的问题后，似乎我的情节没有显示任何数据。请帮我修复情节并检查我的代码中是否有任何错误，谢谢

#function Euler
def euler ( y, t, dt, derivative):
    y_next = y + derivative(y, t) * dt
    return y_next

# function Runge-Kutta
# 2nd order Runge-Kutta method routine

def Runge_Kutta (y, time, dt, derivative):
    k0 = dt * derivative (y, time)
    k1 = dt * derivative (y + k0, time + dt)
    y_next = y + 0.5 * (k0 + k1)
    return y_next

这是我要解决的问题

[![""" A spring and mass  system. the coefficient of friction \mu is not negligible.generate a position vs. time plot for the motion of the mass, given an initial displacement x = 0.2m , spring constant k = 42 N/m , mass m =0.25 Kg, coefficient of friction \mu = 0.15 and initial velocity v = 0

F = -kx +/-mu mg """


from pylab import *
from Runge_Kutta_routine import Runge_Kutta
from eulerODE import euler

N = 500      #input ("How many number of steps to take?")
x0 = 0.2
v0 = 0.0
tau = 3.0     #input ("What is the total time of the simulation in seconds?")
dt = tau /float ( N-1)

k = 41.0      #input (" what is the spring constant?")
m = 0.25      #input ("what is the mass of the bob?")
gravity = 9.8
mu = 0.15     #input ("what is the coefficient of friction?")

""" we create a Nx2 array for storing the results of our calculations. Each 2- element row will be used for the state of the system at one instant, and each instant is separated by time dt. the first element in each row will denote position, the second would be velocity"""

y = zeros (\[N,2\])

y \[0,0\] = x0
y \[0,1\] = v0

def SpringMass (state, time):
    """ we break this second order DE into two first order DE introducing dx/ dt = v & dv/dt = kx/ m +/- mu g....

Note that the direction of the frictional force changes depending on the sign of the velocity, we handle this with an if statement."""


    g0 = state\[1\]
    if g0 > 0:
        g1 = -k/m * state \[0\] - gravity * mu
    else:
        g1 = -k/m * state \[0\] + gravity * mu

    return array (\[g0, g1\])

# Now we do the calculations
# loop only N-1 so that we don;t run into a problem addresssing y\[N+1\] on the last point

    for j in range (N-1):
        #y \[j+1\] = euler ( y\[j\] , 0, dt, SpringMass)
        y \[j+1\] = Runge_Kutta ( y\[j\], 0 , dt, SpringMass)

# Now we plot the result

time = linspace ( 0 , tau, N)
plot ( time, y\[:,0\], 'b-', label ='position')

xlabel('time')
ylabel('position')


show()][1]][1]

Answer 1

看起来以for j in range (N-1):开头的计算数组y的循环是缩进的，因此Python认为这些行是函数SpringMass的一部分。由于这些行在return语句之后，它们永远不会被执行。

要更正此问题，请移动这些行，使for行没有缩进，其他行只有四个缩进空格。看看是否能解决您的问题。

请注意，此处编写的代码仍然无效。在方括号之前有无关的反斜杠，你在一个未命名的模块中编写Euler和Runge_Kutta函数，但主代码期望它们在两个不同的模块中，等等。你也有很多不好的例子样式。这些问题可能是你还没有得到任何（其他）答案的原因。在发布此处和clean up your style之前，请帮助自己并清理代码。

试图通过Euler和Runge_Kutta方法解决二阶DE问题

1 个答案: