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gutter_runner/research/engine_friction.ipynb

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{
"cells": [
{
"cell_type": "code",
"execution_count": 23,
"id": "1002b4fb",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib widget"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "fadc7b33",
"metadata": {},
"outputs": [],
"source": [
"from sympy import Symbol, sin, atan, exp, solve, diff, simplify,Eq\n",
"from sympy.plotting import plot, plot3d"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "3074424c",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "c2fcd32bbbd1482ebe2be970bfe3ed33",
"version_major": 2,
"version_minor": 0
},
"image/png": 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",
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" <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
" Figure\n",
" </div>\n",
" <img 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' width=640.0/>\n",
" </div>\n",
" "
],
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"10"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rpm = Symbol('rpm', positive=True)\n",
"\n",
"friction = pow(rpm - 1000, 4) * 10\n",
"\n",
"plot(friction + 10, (rpm, 1000, 7000))\n",
"\n",
"pow(0, 4) * 10 + 10"
]
}
],
"metadata": {
"kernelspec": {
"display_name": ".venv",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
Reference in New Issue View Git Blame Copy Permalink