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Double pendulum

DoublePendulum.py

@@ -0,0 +1,93 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Wed Apr 18 06:03:32 2018
+
+@author: nolte
+"""
+
+import numpy as np
+from scipy import integrate
+from matplotlib import pyplot as plt
+import time
+
+plt.close('all')
+
+E = 1.       # 1
+
+def flow_deriv(x_y_z_w,tspan):
+    x, y, z, w = x_y_z_w
+
+    A = w**2*np.sin(y-x);
+    B = -2*np.sin(x);
+    C = z**2*np.sin(y-x)*np.cos(y-x);
+    D = np.sin(y)*np.cos(y-x);
+    EE = 2 - (np.cos(y-x))**2;
+
+    FF = w**2*np.sin(y-x)*np.cos(y-x);
+    G = -2*np.sin(x)*np.cos(y-x);
+    H = 2*z**2*np.sin(y-x);
+    I = 2*np.sin(y);
+    JJ = (np.cos(y-x))**2 - 2;
+
+    a = z
+    b = w
+    c = (A+B+C+D)/EE
+    d = (FF+G+H+I)/JJ
+    return[a,b,c,d]
+
+repnum = 75
+
+np.random.seed(1)
+for reploop  in range(repnum):
+
+
+    px1 = 2*(np.random.random((1))-0.499)*np.sqrt(E);
+    py1 = -px1 + np.sign(np.random.random((1))-0.499)*np.sqrt(2*E - px1**2);            
+
+    xp1 = 0.1
+    yp1 = -0.2
+
+    x_y_z_w0 = [xp1, yp1, px1, py1]
+
+    tspan = np.linspace(1,1000,10000)
+    x_t = integrate.odeint(flow_deriv, x_y_z_w0, tspan)
+    siztmp = np.shape(x_t)
+    siz = siztmp[0]
+
+    if reploop % 50 == 0:
+        plt.figure(2)
+        lines = plt.plot(x_t[:,0],x_t[:,1])
+        plt.setp(lines, linewidth=0.5)
+        plt.show()
+        time.sleep(0.1)
+        #os.system("pause")
+
+
+
+    y1 = np.mod(x_t[:,0]+np.pi,2*np.pi) - np.pi
+    y2 = np.mod(x_t[:,1]+np.pi,2*np.pi) - np.pi
+    y3 = np.mod(x_t[:,2]+np.pi,2*np.pi) - np.pi
+    y4 = np.mod(x_t[:,3]+np.pi,2*np.pi) - np.pi
+
+    py = np.zeros(shape=(10*repnum,))
+    yvar = np.zeros(shape=(10*repnum,))
+    cnt = -1
+    last = y1[1]
+    for loop in range(2,siz):
+        if (last < 0)and(y1[loop] > 0):
+            cnt = cnt+1
+            del1 = -y1[loop-1]/(y1[loop] - y1[loop-1])
+            py[cnt] = y4[loop-1] + del1*(y4[loop]-y4[loop-1])
+            yvar[cnt] = y2[loop-1] + del1*(y2[loop]-y2[loop-1])
+            last = y1[loop]
+        else:
+            last = y1[loop]
+
+
+    plt.figure(3)
+    lines = plt.plot(yvar,py,'o',ms=1)
+    plt.show()
+
+
+plt.savefig('DPen')