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started stripping down risk-and-reliability to create template

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Guilherme Alvarenga 2024-02-23 18:02:52 +02:00
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "9d7ffe9f-441f-4119-b5e4-0e872922a78d",
"metadata": {},
"outputs": [],
"source": [
"from sympy import *"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "406dc83e-b114-46be-baf8-073a72b47a36",
"metadata": {},
"outputs": [],
"source": [
"t, a = symbols('t a')\n",
"theta = Function('theta')(t)\n",
"r = Function('r')(t)\n",
"U_c = Function('U_c')(t)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "df8fe246-6986-4ffd-9c39-6bd259176e42",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle - \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\cos{\\left(\\theta{\\left(t \\right)} \\right)}}{r{\\left(t \\right)}}$"
],
"text/plain": [
"-a**2*U_c(t)*cos(theta(t))/r(t)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"phi = - (a**2*U_c)/r * cos(theta)\n",
"phi"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "a6e55454-52c6-493b-a753-f901cee357bc",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\sin{\\left(\\theta{\\left(t \\right)} \\right)} \\frac{d}{d t} \\theta{\\left(t \\right)}}{r{\\left(t \\right)}} + \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\cos{\\left(\\theta{\\left(t \\right)} \\right)} \\frac{d}{d t} r{\\left(t \\right)}}{r^{2}{\\left(t \\right)}} - \\frac{a^{2} \\cos{\\left(\\theta{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{U_{c}}{\\left(t \\right)}}{r{\\left(t \\right)}}$"
],
"text/plain": [
"a**2*U_c(t)*sin(theta(t))*Derivative(theta(t), t)/r(t) + a**2*U_c(t)*cos(theta(t))*Derivative(r(t), t)/r(t)**2 - a**2*cos(theta(t))*Derivative(U_c(t), t)/r(t)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"phi.diff(t)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "52970004-5d18-4905-a61c-01c5d9a7f81c",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\cos{\\left(\\theta{\\left(t \\right)} \\right)}}{r^{2}{\\left(t \\right)}}$"
],
"text/plain": [
"a**2*U_c(t)*cos(theta(t))/r(t)**2"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"phi.diff(r)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "3bc6b6e8-cdba-4eb9-b754-e07cc74c6063",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\sin{\\left(\\theta{\\left(t \\right)} \\right)}}{r^{2}{\\left(t \\right)}}$"
],
"text/plain": [
"a**2*U_c(t)*sin(theta(t))/r(t)**2"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"phi.diff(theta)/r"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bcae9e54-d38d-4128-b872-e4bcb11d19c5",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.9.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}