SciPy 投射物ODE积分

Question

我正在做一个项目，涉及使用SciPy的积分器来模拟这个射击游戏中的抛射物运动。我之前从来没有用过Python编程，而且我的微积分有点生疏，不过经过几个小时的努力，我发现很难确定到底是什么导致了某些错误。在经过几小时的反复尝试后，我让它在积分方法中工作了（我觉得这是欧拉积分，但老实说我不太确定）。不过我还需要使用SciPy库中的两个积分器，但它们一直没有工作。两个积分器在同一个地方都抛出了相同的错误信息：

"  File "**file extension**", line 17, in eq
    projX = x[0];
   TypeError: 'float' object has no attribute '__getitem__'"

看起来它期待的是不同类型的对象，但老实说我不知道该怎么理解。我不确定是我用错了积分器，还是在设置常微分方程（ODE）时犯了错误。我真的很困惑。任何帮助都会非常感激。以下是代码：

from numpy import *
from scipy.integrate import ode
from scipy import *

# setup wind (it will be replaced with the current value of the wind at every
# instant in time) 
wd = array([0, 0])

# computes the ODE
def eq(x, t):

  # setup gravitational acceleration
  #this is Acceleration for Y
  GRAVITY = 9.81

  # get out the positions and velocities
  projX = x[0];
  projY = x[1];
  projVX = x[2];
  projVY = x[3];

  # TODO: setup the acceleration 
   #acceleration is the derivitive of velocity (VX..VY acceleration is GRAVITY) in this case        it's 0 (no wind)?
  ACCELERATION = 0 #will be effected by wind


  #TODO ground force

  # TODO: return appropriate things
  #needs to return: (x,y Time derivatives and x,y acceleration)
  #acceleration is  derivative of velocity. Velocity derivative of position.
 #is essentially dx/dt
  return array([x[2], x[3], ACCELERATION, -GRAVITY])


# integrates a projectile forward in time using simple Euler integration
# t:  the current time of the system
# dt: the time to step the system forward
# x:  the current state of the system ([x position, y position, x velocity, y
#     velocity)
# returns the new state of the system
def integrate(t, dt, x):
    #Euler Method
    #x[0] = x[0] + x[2]*dt
    #x[2] = x[2]
    #x[1] = x[1]+x[3]*dt
    #x[3] = x[3]-(9.81*dt)

    #SciPy Dopri5 Integration

    #vode Integrator
    method = ode(eq).set_integrator('vode', method = 'bdf')
    method.set_initial_value(x, t)
    method.integrate(method.t+dt)
    return x
    #write one function that represents one step of the diff equation

它是从projectile.py中调用的。大部分代码只是为了绘图和设置PyGame，但与这部分相关的代码片段是：

      # integrate the projectile forward in time
  x = dynamics.integrate(fireT, dt, array([projX, projY, projVX, projVY]))
  projX = x[0]
  projY = x[1]
  projVX = x[2]
  projVY = x[3]

  # update the time
  fireT = fireT + dt

scipy 编程错误数值模拟常微分方程 ode 积分器抛射物运动欧拉积分

SciPy 投射物ODE积分

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