Skip to content
Open
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
120 changes: 120 additions & 0 deletions projects/velocity_verlet_rope_philip.ipynb
Original file line number Diff line number Diff line change
@@ -0,0 +1,120 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from __future__ import division"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"#10 particles in 15m height\n",
"init_pos=np.array([np.array([2*i,15])for i in range(10)])\n",
"init_vel=np.zeros(init_pos.shape)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"def normalize(a):\n",
" return a/np.linalg.norm(a)\n",
"\n",
"def acceleration(index,pos,k=300,g=9.81,m=1):\n",
" a=pos[index]\n",
" n_1,n_2=pos[index-1],pos[index+1]\n",
" a_grav=[0,-g]\n",
" a_spring1=-k*(a-n_1)/m\n",
" a_spring2=-k*(a-n_2)/m\n",
" total_a= a_grav+a_spring1+a_spring2\n",
" return total_a\n",
"def velocity_verlet(timestep,totaltime):\n",
" n=int(totaltime/timestep)\n",
" pos=np.array([np.array([2*i,15])for i in range(10)])\n",
" vel=np.zeros(init_pos.shape)\n",
" for i in range(n):\n",
" oldpos=pos\n",
" for j in range(1,len(pos)-1):\n",
" new_pos=pos[j]+timestep*vel[j]+timestep**2*acceleration(j,pos)/2\n",
" pos[j]=new_pos\n",
" new_vel=vel[j]+timestep*(acceleration(j,oldpos)+acceleration(j,pos))\n",
" vel[j]=new_vel\n",
" \n",
" \n",
"\n",
" x,y=pos.swapaxes(0,1)[0],pos.swapaxes(0,1)[1]\n",
" plt.plot(x,y,ls=':',marker='o')\n",
" plt.show()\n",
"\n",
" \n",
" "
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x6a32b50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"velocity_verlet(0.001,10)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.14"
}
},
"nbformat": 4,
"nbformat_minor": 2
}