Python Slingshot模型

Question

我正在尝试模拟从弹弓发射投射物的模型。

这是我的代码：

from pylab import * 
import numpy as np
from scipy.integrate import odeint
import seaborn
## set initial conditions and parameters
g = 9.81            # acceleration due to gravity
th = 30            # set launch angle
th = th * np.pi/180.   # convert launch angle to radians
v0 = 10.0           # set initial speed
c = 0.5             # controls strength of air drag
d = 0.02 # diameter of the spherical rock
A = pi * (d/2)**2 #the cross-sectional area of the spherical rock
ro = 1.2041 #the density of the medium we are perfoming the launch in
m = 0.01 #mass

x0=0                # specify initial conditions
y0=0
vx0 = v0*sin(th)
vy0 = v0*cos(th)

## defining our model
def slingshot_model(state,time):
    z = zeros(4)    # create array to hold z vector
    z[0] = state[2] # z[0] = x component of velocity
    z[1] = state[3] # z[1] = y component of velocity
    z[2] = - c*A*ro/2*m*sqrt(z[0]**2 + z[1]**2)*z[0]         # z[2] = acceleration in x direction
    z[3] = -g/m - c*A*ro/2*m*sqrt(z[0]**2 + z[1]**2)*z[1]       # z[3] = acceleration in y direction
    return z

## set initial state vector and time array
X0 = [x0, y0, vx0, vy0]        # set initial state of the system
t0 = 0
tf = 4 #final time
tau = 0.05 #time step


# create time array starting at t0, ending at tf with a spacing tau
t = arange(t0,tf,tau)   

## solve ODE using odeint
X = odeint(slingshot_model,X0,t) # returns an 2-dimensional array with the 
                        # first index specifying the time and the
                        # second index specifying the component of
                        # the state vector

# putting ':' as an index specifies all of the elements for
# that index so x, y, vx, and vy are arrays at times specified 
# in the time array
x = X[:,0]  
y = X[:,1] 
vx = X[:,2] 
vy = X[:,3]

plt.rcParams['figure.figsize'] = [10, 10]
plot(x,y)

但它给了我一个对我来说没有意义的情节：

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我遗漏了什么？价值观不应该像他们那样出现，但对于我的生活来说，我不明白为什么。

这可能是一些微不足道的事情，但我已经盯着它看了太久，所以我认为引入一组新的眼睛是最好的行动方案。

Answer 1

我认为你的计算至少有两个主要问题：

1. 通常是根据X-axis来定义的。因此

vx0 = v0*cos(th) # not sin vy0 = v0*sin(th) # not cos

• 最重要的是，为什么要将自由落体加速度除以质量g？(参见z[3] = -g/m...)这对我来说毫无意义。不要除以质量！

编辑：

基于您的注释和链接公式，很明显，您的代码还存在第三个错误:空气阻力项应该与mass成反比(

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