CoCalc -- pendulo.ipynb

Jupyter notebook pendulo.ipynb

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Kernel: Python 2

In [4]:

from numpy import *
from scipy import *
from scipy.integrate import *
from pylab import *
%matplotlib inline

\ddot \theta + \sqrt{\frac{g}{l}} \sin \theta = 0

Convertiendo a un sistema de ecuaciones: $\dot \theta = v_{\theta}$ $\dot v_{\theta}= -\sqrt{\frac{g}{l}} \sin \theta$ Mis variables sin la pareja ordenada $(\theta , v_{\theta})$

In [14]:

def pendulo(vec_r, t, g=9.8 , l=1.0):
    return [ vec_r[1], -sqrt(g/l)*sin(vec_r[0])]

In [5]:

pendulo([0, pi/2, pi], g=9.8, l=1.0)

Out[5]:

[1.5707963267948966, -0.0]

In [15]:

tiempo= linspace(0,2*pi)
cond_ini = [0, 1]
solucion = odeint(pendulo, cond_ini, tiempo)
plot(tiempo,solucion[:,0], tiempo,solucion[:,1] )

Out[15]:

[<matplotlib.lines.Line2D at 0x106e78e50>,
 <matplotlib.lines.Line2D at 0x106e85110>]

In [16]:

plot(solucion[:,0],solucion[:,1])

Out[16]:

[<matplotlib.lines.Line2D at 0x107090950>]

In [9]:

print solucion[:,0]

Out[9]:

[ 0.          0.19198671  0.38069649  0.56079901  0.72594114  0.86957723
  0.9855581   1.06848641  1.11386789  1.11814592  1.07874473  0.99425063
  0.86482821  0.69289004  0.48389662  0.24697693 -0.00506707 -0.25670056
 -0.49144808 -0.69394468 -0.85149477 -0.954732   -0.99752147 -0.97659837
 -0.89146166 -0.74483559 -0.5436674  -0.30018374 -0.03213716  0.23856288
  0.4888144   0.697741    0.84908629  0.93194348  0.94033381  0.87267343
  0.73194428  0.52673988  0.27253553 -0.00815899 -0.28797839 -0.53900755
 -0.73729008 -0.86547347 -0.9131573  -0.87613396 -0.75603428 -0.56112506
 -0.30777362 -0.02092843]

In [18]:

tiempo = linspace(0,5*pi,200)
N=50
for i in range(N):
    cond_ini=[rand(),rand()]
    solucion =odeint(pendulo, cond_ini,tiempo)
    plot(solucion[:,0],solucion[:,1])

Out[18]:

In [ ]:

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