103 lines
2.5 KiB
Plaintext
103 lines
2.5 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\left[\\begin{matrix}0 & 0 & - v \\sin{\\left(\\theta \\right)} & 0 & 0\\\\0 & 0 & v \\cos{\\left(\\theta \\right)} & 0 & 0\\\\0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & - v \\cos{\\left(\\psi \\right)} & 0\\end{matrix}\\right]$"
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],
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"text/plain": [
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"Matrix([\n",
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"[0, 0, -v*sin(theta), 0, 0],\n",
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"[0, 0, v*cos(theta), 0, 0],\n",
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"[0, 0, 0, 0, 0],\n",
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"[0, 0, 0, 0, 0],\n",
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"[0, 0, 0, -v*cos(psi), 0]])"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"import sympy as sp\n",
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"\n",
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"x,y,theta,psi,cte,v,w = sp.symbols(\"x y theta psi cte v w\")\n",
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"\n",
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"gs = sp.Matrix([[ sp.cos(theta)*v],\n",
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" [ sp.sin(theta)*v],\n",
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" [w],\n",
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" [w],\n",
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" [ v*sp.sin(-psi)]])\n",
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"\n",
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"state = sp.Matrix([x,y,theta,psi,cte])\n",
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"\n",
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"gs.jacobian(state)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\left[\\begin{matrix}\\cos{\\left(\\theta \\right)} & 0\\\\\\sin{\\left(\\theta \\right)} & 0\\\\0 & 1\\\\0 & 1\\\\- \\sin{\\left(\\psi \\right)} & 0\\end{matrix}\\right]$"
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],
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"text/plain": [
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"Matrix([\n",
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"[cos(theta), 0],\n",
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"[sin(theta), 0],\n",
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"[ 0, 1],\n",
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"[ 0, 1],\n",
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"[ -sin(psi), 0]])"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"state = sp.Matrix([v,w])\n",
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"\n",
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"gs.jacobian(state)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.9"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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