我不知道为什么python会抛出这个错误

Question

我正在尝试创建一个程序，该程序绘制自由落体中球的速度与暴露于阻力的球的速度，使得 F_drag = -Cv^2 其中 C 是常数 (m*g)/100。我的输入是 5 代表 m，5 代表 tf，0.1 代表 dt。import numpy as npimport matplotlib.pyplot as plt%matplotlib inlinem = float(input("Input the mass of the ball in kilograms: "))tf = float(input("Input a specified time of fall in seconds: "))dt = float(input("Input the time step for each calculation in seconds: "))imaxFloat = tf/dt   # The total number of time steps as a floating point number with remainderimax = int(round(imaxFloat))   # Converts the float to the nearest integer v0 = 0       # Velocity at t = 0g = 9.8       # Accleration due to gravityi = 0       # Initial counter valuei2 = 0     # Initial counter value 2c = (m*g)/100     # Constant in drag equationt1 = np.array([0])v1 = np.array([v0])t2 = np.array([0])v2 = np.array([v0])drag_a = ((m*g)-(c*v1*v1))/m     # Acceleration of ball with dragwhile i < imax:    t1 = np.append(t1, t1[i] + dt)    v1 = np.append(v1, v1[i] - g * dt )    i = i + 1while i2 < imax:    t2 = np.append(t2, t2[i] + dt)    v2 = np.append(v2, v2[i] - drag_a * dt)    i2 = i2 + 1plt.plot(t1, v1, label = "Neglecting air resistance")plt.plot(t2, v2, label = "With air resistance")Python 抛出此错误：---------------------------------------------------------------------------IndexError                                Traceback (most recent call last)<ipython-input-6-10c7e3224e87> in <module>     30      31 while i2 < imax:---> 32     t2 = np.append(t2, t2[i] + dt)     33     v2 = np.append(v2, v2[i] - drag_a * dt)     34     i2 = i2 + 1IndexError: index 50 is out of bounds for axis 0 with size 1我一般需要帮助解决这个问题，但也需要找到解决这个错误的方法。谢谢！

Answer 1

你的 while 循环真的不应该使用np.append. 它很慢。

In [119]: t1 = np.array([0]) 

     ...: i=0 

     ...: while i < 10: 

     ...:     t1 = np.append(t1, t1[i] + .1) 

     ...:     i += 1 

     ...:                                                                       

In [120]: t1                                                                    

Out[120]: array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])

列表追加更快：

In [121]: t1 = [0] 

     ...: i=0 

     ...: for i in range(10): 

     ...:     t1.append(t1[-1] + .1)     # t1[-1] the last, latest, value

     ...:      

     ...:                                                                       

In [122]: t1                                                                    

Out[122]: 

[0,

 0.1,

 0.2,

 0.30000000000000004,

 0.4,

 0.5,

 0.6,

 0.7,

 0.7999999999999999,

 0.8999999999999999,

 0.9999999999999999]

In [123]: np.array(_)                                                           

Out[123]: array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])

更好的是使用arange：

In [124]: np.arange(11)*0.1                                                     

Out[124]: array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])

In [127]: np.linspace(0,1,11)                                                   

Out[127]: array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])

Answer 2

在第二个 while 循环中，您应该将其i2用作索引变量。由于在循环的第一次迭代中，t2[i]是真的t2[50]，但当时t2只有一个元素，所以索引超出了范围。

import numpy as np

import matplotlib.pyplot as plt

%matplotlib inline

m = float(input("Input the mass of the ball in kilograms: "))

tf = float(input("Input a specified time of fall in seconds: "))

dt = float(input("Input the time step for each calculation in seconds: "))

imaxFloat = tf/dt   # The total number of time steps as a floating point number with remainder

imax = int(round(imaxFloat))   # Converts the float to the nearest integer 

v0 = 0       # Velocity at t = 0

g = 9.8       # Accleration due to gravity

i = 0       # Initial counter value

i2 = 0     # Initial counter value 2

c = (m*g)/100     # Constant in drag equation

t1 = np.array([0])

v1 = np.array([v0])

t2 = np.array([0])

v2 = np.array([v0])

drag_a = ((m*g)-(c*v1*v1))/m     # Acceleration of ball with drag

while i < imax:

    t1 = np.append(t1, t1[i] + dt)

    v1 = np.append(v1, v1[i] - g * dt )

    i = i + 1

while i2 < imax:

    t2 = np.append(t2, t2[i2] + dt)

    v2 = np.append(v2, v2[i2] - drag_a * dt)

    i2 = i2 + 1

plt.plot(t1, v1, label = "Neglecting air resistance")

plt.plot(t2, v2, label = "With air resistance")