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funciones.py
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from numpy import *
from matplotlib.pyplot import *
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
from pylab import meshgrid,cm,imshow,contour,clabel,colorbar,axis,title,show
from scipy.integrate import odeint
import seaborn as sns
sns.set_theme()
def H(a, p, pa, pp):
ac, pc, pac, ppc = a**2, p**2, pa**2, pp**2
return
def V(a, p, m, k):
ac, pc, mc = a**2, p**2, m**2
return 0.5*(k*pc - k*ac + mc*ac*pc)
def ecuaciones(x, t, m, k):
a, p, pa, pp = x[0], x[1], x[2], x[3]
ac, pc, mc = a**2, p**2, m**2
return [-pa, pp, a*(k - mc*pc), -p*(k + mc*ac)]
def modelo(x, n, dt, m):
mc = m**2
t, a, p, pa, pp = x[0], x[1], x[2], x[3], x[4]
for i in range(n):
ac, pc = a[i]**2, p[i]**2
t.append(t[i]+dt)
a.append(a[i] - pa[i]*dt)
p.append(p[i] + pp[i]*dt)
pa.append(pa[i] + a[i]*(1 + mc*pc)*dt)
pp.append(pp[i] + p[i]*(1 - mc*ac)*dt)
return t, [a, p, pa, pp]
def dinamica(x0, t, m, k):
t0 = np.arange(t[0], t[1], t[2])
return t0, odeint(ecuaciones, x0, t0, args=(m,k))
def superficie(f, xi, xf, yi, yf, n, m, k):
x = linspace(xi,xf,n)
y = linspace(yi,yf,n)
X, Y = meshgrid(x, y)
Z = f(X, Y, m, k)
return [X,Y,Z,x,y]
def poincare(a0, p0, pp0, t, m, k):
V0 = V(a0, p0, m, k) #Potencial en el punto inicial
pa0 = sqrt(pp0**2 + 2*V0)
x0 = [a0, p0, pa0, pp0] #Vector de estado inicial
t0, sol = dinamica(x0, t, m, k)
a, p, pa, pp = sol[:, 0], sol[:, 1], sol[:, 2], sol[:, 3]
prueba = 0.0
zeros = array([[],[]])
i = 0
while i < (a.shape[0]-1):
if ((a[i] < prueba) and (a[i+1] > prueba)) or ((a[i] > prueba) and (a[i+1] < prueba)):
puntos = array([[0.5*(p[i]+p[i+1])], [0.5*(pp[i]+pp[i+1])]])
zeros = hstack((zeros,puntos))
i = i + 1
return zeros
def cor(a0, p0, pp0, t, m, k):
V0 = V(a0, p0, m, k) #Potencial en el punto inicial
pa0 = sqrt(pp0**2 + 2*V0)
x0 = [a0, p0, pa0, pp0] #Vector de estado inicial
t0, sol = dinamica(x0, t, m, k)
a, p, pa, pp = sol[:, 0], sol[:, 1], sol[:, 2], sol[:, 3]
prueba = 0.0
zeros = array([[],[]])
i = 0
while i < (a.shape[0]-1):
if ((a[i] < prueba) and (a[i+1] > prueba)) or ((a[i] > prueba) and (a[i+1] < prueba)):
puntos = array([[0.5*(p[i]+p[i+1])], [0.5*(pp[i]+pp[i+1])]])
zeros = hstack((zeros,puntos))
i = i + 1
return zeros
def orbita(a0, p0, pp0, t, m, k):
V0 = V(a0, p0, m, k)
pa0 = sqrt(pp0**2+ 2*V0)
x = [a0, p0, pa0, pp0]
t0, sol = dinamica(x, t, m, k)
return sol
def lyapunov(a0, p0, pp0, t, d, m, k):
V0 = V(a0, p0, m, k)
pa0 = sqrt(pp0**2 + 2*V0)
x = [a0,p0,pa0,pp0]
t0, Sol = dinamica(x, t, m, k)
V0d = V(a0+d, p0, m, k)
pa0d = sqrt(pp0**2 + 2*V0d)
xd = [a0+d, p0, pa0d, pp0]
t0, Sold = dinamica(xd, t, m, k)
da0, dp0, dpa0, dpp0 = d, 0, pa0d - pa0, 0
a, p, pa, pp = Sol[:, 0], Sol[:, 1], Sol[:, 2], Sol[:, 3]
ad, pd, pad, ppd = Sold[:, 0], Sold[:, 1], Sold[:, 2], Sold[:, 3]
da, dp, dpa, dpp = ad-a, pd-p, pad-pa, ppd-pp
s0 = sqrt(da0**2 + dp0**2 + dpa0**2 + dpp0**2)
s = sqrt(da**2 + dp**2 + dpa**2 + dpp**2)
Lambda = (log(s/(s0)))/(t0)
return [Lambda,t0]
def graph2D(Sol, p, m):
figure()
plot(Sol[:,0],Sol[:,1],linewidth=0.1)
xlabel('$a$')
ylabel('$\\varphi$')
savefig('C:\\Users\\juan1\\Downloads\\ProyectoFinal\\Imagenes\\orbitas2d_pp'+str(p)+'_m'+str(m)+'.png')
show()
def graph3D(Sol, p, m):
fig = figure()
ax = fig.add_subplot(111, projection='3d')
cset = ax.plot(Sol[:,1],Sol[:,0],Sol[:,3],linewidth=0.1)
ax.clabel(cset, fontsize=9, inline=1)
ax.set_xlabel('$\\varphi$')
ax.set_ylabel('$a$')
ax.set_zlabel('$P_\\varphi$')
savefig('C:\\Users\\juan1\\Downloads\\ProyectoFinal\\Imagenes\\orbitas3d_pp'+str(p)+'_m'+str(m)+'.png')
show()
def g(x, y, *args):
plot(x, y)
title(args[0])
xlabel(args[1])
ylabel(args[2])
if args[3]:
savefig(args[4])
show()