__author__ Lenovo import numpy as np np pi v0 30 l1 np sin v0 print fl

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
__author__ = 'Lenovo'
import numpy as np
a = np.pi / 4
g = 9.8
v0 = 30
l1 = np.sin(2*a) * v0 ** 2 / g
print 'flight length in Galiley model:' + str(l1)
ro = 7600
r = 0.2
u = v0 * np.cos(a)
w = v0 * np.sin(a)
h = 0.01
b = 0.16 * 1.15 * np.pi * r * r / 2.0
m = ro * 4 * np.pi * r * r * r /3
x = 0
y = 0
f = False
xprev = 0
yprev = 0
def deriv_u_t(u, w):
return (-b) * u * np.sqrt(u**2 + w**2) / m
def deriv_w_t(u, w):
return -g - b * w * np.sqrt(u**2 + w**2) / m
while (True):
k1u = h * deriv_u_t(u, w)
k1w = h * deriv_w_t(u, w)
k2u = h * deriv_u_t(u + h * k1u/2, w + h * k1w/2)
k2w = h * deriv_w_t(u + h * k1u/2, w + h * k1w/2)
k3u = h * deriv_u_t(u + h * k2u/2, w + h * k2w/2)
k3w = h * deriv_w_t(u + h * k2u/2, w + h * k2w/2)
k4u = h * deriv_u_t(u + h * k3u, w + h * k3w)
k4w = h * deriv_w_t(u + h * k3u, w + h * k3w)
u += (k1u + 2 * k2u + 2 * k3u + k4u)/6
w += (k1w + 2 * k2w + 2 * k3w + k4w)/6
v = np.sqrt(u**2 + w**2)
xprev = x
yprev = y
x += u * h
y += w * h
if (y == 0):
f = True
break
if (y < 0):
break
print 'flight length in Newton model:'
if (f):
print x
else:
print (xprev * y - x * yprev) / (y - yprev)