From 08123b0d15395725741f73436a244e12359313cb Mon Sep 17 00:00:00 2001
From: Roger Labbe <rlabbejr@gmail.com>
Date: Fri, 1 May 2015 07:05:53 -0700
Subject: [PATCH] Regenerated PDF

---
 06_Multivariate_Kalman_Filters.ipynb   |  3 +-
 Appendix_B_Symbols_and_Notations.ipynb |  7 +++-
 experiments/bicycle.py                 | 46 ++++++++++++++++++++++++++
 experiments/euler.py                   | 26 +++++++++++++++
 4 files changed, 80 insertions(+), 2 deletions(-)
 create mode 100644 experiments/bicycle.py
 create mode 100644 experiments/euler.py

diff --git a/06_Multivariate_Kalman_Filters.ipynb b/06_Multivariate_Kalman_Filters.ipynb
index b72a09f..7aa2921 100644
--- a/06_Multivariate_Kalman_Filters.ipynb
+++ b/06_Multivariate_Kalman_Filters.ipynb
@@ -388,7 +388,8 @@
    "cell_type": "code",
    "execution_count": 11,
    "metadata": {
-    "collapsed": false
+    "collapsed": false,
+    "scrolled": true
    },
    "outputs": [
     {
diff --git a/Appendix_B_Symbols_and_Notations.ipynb b/Appendix_B_Symbols_and_Notations.ipynb
index 4e83e76..c049a21 100644
--- a/Appendix_B_Symbols_and_Notations.ipynb
+++ b/Appendix_B_Symbols_and_Notations.ipynb
@@ -102,7 +102,7 @@
        "        color: #1d3b84;\n",
        "        font-size: 16pt;\n",
        "        margin-bottom: 0em;\n",
-       "        margin-top: 1.5em;\n",
+       "        margin-top: 0.5em;\n",
        "        display: block;\n",
        "        white-space: nowrap;\n",
        "    }\n",
@@ -126,6 +126,11 @@
        "        overflow-y: scroll;\n",
        "        max-height: 50000px;\n",
        "    }\n",
+       "    div.output_wrapper{\n",
+       "        margin-top:0.2em;\n",
+       "        margin-bottom:0.2em;\n",
+       "}\n",
+       "\n",
        "    code{\n",
        "      font-size: 70%;\n",
        "    }\n",
diff --git a/experiments/bicycle.py b/experiments/bicycle.py
new file mode 100644
index 0000000..76efdb4
--- /dev/null
+++ b/experiments/bicycle.py
@@ -0,0 +1,46 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Apr 28 08:19:21 2015
+
+@author: Roger
+"""
+
+
+from math import *
+import numpy as np
+import matplotlib.pyplot as plt
+
+wheelbase = 100 #inches
+
+vel = 20 *12  # fps to inches per sec
+steering_angle = radians(1)
+t = 1 # second
+orientation = 0. # radians
+
+pos = np.array([0., 0.])
+
+
+for i in range(100):
+#if abs(steering_angle) > 1.e-8:
+    dist = vel*t
+    turn_radius = tan(steering_angle)
+    radius = wheelbase / tan(steering_angle)
+    
+    arc_len = dist / (2*pi*radius)
+    
+    turn_angle = 2*pi * arc_len
+    
+    
+    cx = pos[0] - (sin(orientation) * radius)
+    cy = pos[1] + (cos(orientation) * radius)
+    
+    orientation = (orientation + turn_angle) % (2.0 * pi)
+    pos[0] = cx + (sin(orientation) * radius)
+    pos[1] = cy - (cos(orientation) * radius)
+
+    plt.scatter(pos[0], pos[1])
+
+plt.axis('equal')
+   
+   
+   
\ No newline at end of file
diff --git a/experiments/euler.py b/experiments/euler.py
new file mode 100644
index 0000000..d9e6b2b
--- /dev/null
+++ b/experiments/euler.py
@@ -0,0 +1,26 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Apr 21 18:40:47 2015
+
+@author: Roger
+"""
+
+
+
+
+def dx(t, y):
+    return y
+    
+    
+def euler(t0, tmax, y0, dx, step=1.):
+    t = t0
+    y = y0
+    while t < tmax:
+        f = dx(t,y)
+        y = y + step*dx(t, y)
+        t +=step
+        
+    return y
+    
+    
+print(euler(0, 4, 1, dx, step=0.25))
\ No newline at end of file