I am just playing with python's scientific libraries expecially the examples from here: http://faculty1.coloradocollege.edu/~sburns/toolbox/ODE_II.html
I modified it by defining a "force function" and tried to make a simple (but non physical example) where the force depends on the x and y position of the object. Additionally I want to plot the force field with quiever. The problem is that I don't understand how to make the force function properly depend on (a function of) the x and y components of the position of the object, especially I get the error cited below.
from pylab import *
from scipy.integrate import odeint
import numpy as np
## set initial conditions and parameters
g = 9.81 # acceleration due to gravity
th = 91 # set launch angle
th = th * pi/180. # convert launch angle to radians
v0 = 100 # set speed
x0=0 # specify initial conditions
y0=0
vx0 = v0*sin(th)
vy0 = v0*cos(th)
## define force Funktion
def F_func(x):
F = zeros(2)
F[0] = x[1] #
F[1] = x[0] #
return F
## define function to compute f(X,t)
def f_func(state,time):
f = zeros(4) # create array to hold f vector
f[0] = state[2] # f[0] = x component of velocity
f[1] = state[3] # f[1] = x component of velocity
f[2] = F_func(state[:2])[0] # f[2] = acceleration in x direction
f[3] = F_func(state[:2])[1] # f[3] = acceleration in y direction
return f
## set initial state vector and time array
X0 = [ x0, y0, vx0, vy0] # set initial state of the system
t0 = 0.
tf = 10
tau = 0.1
#tf = input("Enter final time: ")
#tau = input("Enter 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(f_func,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
print X
# 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]
## plot the trajectory
fig = figure()
ax = fig.add_subplot(1,1,1)
## Enlarge Limits by en Percent
en = 0.05
#xMin,xMax = 0,10
xMin,xMax = min(x),max(x)
yMin,yMax = min(y),max(y)
xMin,xMax = xMin - (xMax-xMin)*en,xMax + (xMax-xMin)*en
yMin,yMax = yMin - (yMax-yMin)*en,yMax + (yMax-yMin)*en
#plot(x,y,[xMin,xMax],[yMin,yMax])
#plot(x,y,[0,10],[0,10])
ax.plot(x,y)
ax.axis('tight')
xlim([xMin,xMax])
ylim([yMin,yMax])
xG,yG = meshgrid(linspace(xMin,xMax,10),linspace(yMin,yMax,5))
ax.quiver(xG,yG,F_func(zip(xG,yG))[0],F_func(zip(xG,yG))[1],pivot='middle',minshaft=5,minlength=1,alpha=0.1)
xlabel('x')
ylabel('y')
show()
With this code I get the following error:
ValueError Traceback (most recent call last)
/usr/lib/python2.7/dist-packages/IPython/utils/py3compat.pyc in execfile(fname, *where)
176 else:
177 filename = fname
--> 178 __builtin__.execfile(filename, *where)
/home/myuser/python/test.py in <module>()
87 xG,yG = meshgrid(linspace(xMin,xMax,10),linspace(yMin,yMax,5))
88
---> 89 ax.quiver(xG,yG,F_func(zip(xG,yG))[0],F_func(zip(xG,yG))[1],pivot='middle',minshaft=5,minlength=1,alpha=0.1)
90
91
/home/myuser/python/test.py in F_func(x)
20 def F_func(x):
21 F = zeros(2)
---> 22 F[0] = x[1] #
23 F[1] = x[0] #
24 return F
ValueError: setting an array element with a sequence.
Can somebody explain this and how to fix it?
