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{
"cells": [
{
"cell_type": "code",
"execution_count": 49,
"id": "1fdd6e8c-7edc-4174-bf9b-66b51e152187",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T14:16:40.899000+01:00",
"iopub.status.busy": "2022-01-28T14:16:40.899000+01:00",
"iopub.status.idle": "2022-01-28T14:16:52.581000+01:00",
"shell.execute_reply": "2022-01-28T14:16:52.581000+01:00"
},
"tags": []
},
"outputs": [],
"source": [
"using DifferentialEquations\n",
"using LinearAlgebra\n",
"using PyPlot"
]
},
{
"cell_type": "code",
"execution_count": 183,
"id": "3a008a45-b9bc-46e5-a6c0-1770d0640d9b",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T15:58:54.608000+01:00",
"iopub.status.busy": "2022-01-28T15:58:54.608000+01:00",
"iopub.status.idle": "2022-01-28T15:58:54.616000+01:00",
"shell.execute_reply": "2022-01-28T15:58:54.616000+01:00"
},
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"eqmotion! (generic function with 1 method)"
]
},
"execution_count": 183,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function eqmotion!(du, u ,p ,t)\n",
" d, n, m = p\n",
" \n",
" dn = d * n\n",
" for i in 1:dn\n",
" du[i] = u[i+dn]\n",
" end\n",
" \n",
" for i in 1:n\n",
" x = view( u, (i-1)*d .+ (1:d))\n",
" v = view( u, dn + (i-1)*d .+ (1:d))\n",
" a = view(du, dn + (i-1)*d .+ (1:d))\n",
" a .= 0.0\n",
" for j = 1:n\n",
" i == j && continue\n",
" y = view(u, (j-1)*d .+ (1:d))\n",
" r = norm(x - y)\n",
" a .+= m[j] * (y - x) / r^3 \n",
" end\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 196,
"id": "b9626e8f-b30c-4f06-9f9b-df44ff5913dd",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T16:04:47.363000+01:00",
"iopub.status.busy": "2022-01-28T16:04:47.363000+01:00",
"iopub.status.idle": "2022-01-28T16:04:47.365000+01:00",
"shell.execute_reply": "2022-01-28T16:04:47.365000+01:00"
},
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"(2, 2, [1000, 1])"
]
},
"execution_count": 196,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p = (2, 2, [1000,1])"
]
},
{
"cell_type": "code",
"execution_count": 197,
"id": "e1666635-152a-4ea6-943b-2d779c2f4b8e",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T16:04:47.495000+01:00",
"iopub.status.busy": "2022-01-28T16:04:47.495000+01:00",
"iopub.status.idle": "2022-01-28T16:04:47.496000+01:00",
"shell.execute_reply": "2022-01-28T16:04:47.496000+01:00"
},
"tags": []
},
"outputs": [],
"source": [
"u0 = Float64[0, 0, 10, 0, 0, 0, 0, 10];"
]
},
{
"cell_type": "code",
"execution_count": 198,
"id": "87788815-3d27-4798-9acb-6fa8edfdbdc1",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T16:04:47.672000+01:00",
"iopub.status.busy": "2022-01-28T16:04:47.672000+01:00",
"iopub.status.idle": "2022-01-28T16:04:47.685000+01:00",
"shell.execute_reply": "2022-01-28T16:04:47.685000+01:00"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"length(sol.t) = 1001\n"
]
}
],
"source": [
"tspan = (0, 10)\n",
"sol = solve(ODEProblem(eqmotion!, u0, tspan, p), \n",
" abstol=1e-10,\n",
" reltol=1e-10,\n",
" saveat=0.01);\n",
"\n",
"@show length(sol.t);"
]
},
{
"cell_type": "code",
"execution_count": 191,
"id": "a0ee99af-d83c-4504-a3d9-a172998e1874",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T16:02:19.264000+01:00",
"iopub.status.busy": "2022-01-28T16:02:19.263000+01:00",
"iopub.status.idle": "2022-01-28T16:02:19.435000+01:00",
"shell.execute_reply": "2022-01-28T16:02:19.435000+01:00"
},
"tags": []
},
"outputs": [
{
"data": {
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",
"text/plain": [
"Figure(PyObject <Figure size 640x480 with 1 Axes>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for k in 1:p[2]\n",
" plot(getindex.(sol.u, (k-1)*p[1] + 1), getindex.(sol.u, (k-1)*p[1] + 2), label = \"M$k\")\n",
"end\n",
"legend();"
]
},
{
"cell_type": "markdown",
"id": "d41fc209-f4f9-442c-887a-7a29c83bb479",
"metadata": {},
"source": [
"## 3 bodies in 2 dimnsions"
]
},
{
"cell_type": "code",
"execution_count": 192,
"id": "fbcaba0a-c998-4bd9-984b-fcd816acba9f",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T16:02:35.877000+01:00",
"iopub.status.busy": "2022-01-28T16:02:35.876000+01:00",
"iopub.status.idle": "2022-01-28T16:02:35.879000+01:00",
"shell.execute_reply": "2022-01-28T16:02:35.879000+01:00"
},
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"(2, 3, [1000, 10, 50])"
]
},
"execution_count": 192,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p = (2, 3, [1000,10,50])"
]
},
{
"cell_type": "code",
"execution_count": 193,
"id": "6eea0bda-7bf5-4f33-8457-52593dd5ad62",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T16:02:37.809000+01:00",
"iopub.status.busy": "2022-01-28T16:02:37.808000+01:00",
"iopub.status.idle": "2022-01-28T16:02:37.813000+01:00",
"shell.execute_reply": "2022-01-28T16:02:37.813000+01:00"
},
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"0.0"
]
},
"execution_count": 193,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"u0 = Float64[ 0, 0, 10, 0, 0, 10, 0, 0, 0, 6, -3, 0];\n",
"du = similar(u0);\n",
"t = 0.0"
]
},
{
"cell_type": "code",
"execution_count": 194,
"id": "be1b4bb2-055c-4ed8-9382-43365ff85b6f",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T16:02:41.139000+01:00",
"iopub.status.busy": "2022-01-28T16:02:41.138000+01:00",
"iopub.status.idle": "2022-01-28T16:02:52.537000+01:00",
"shell.execute_reply": "2022-01-28T16:02:52.537000+01:00"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"length(sol.t) = 7001\n"
]
},
{
"data": {
"text/plain": [
"7001"
]
},
"execution_count": 194,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tspan = (0, 7)\n",
"sol = solve(ODEProblem(eqmotion!,u0,tspan,p), \n",
" abstol=1e-10,\n",
" reltol=1e-10,\n",
" saveat=0.001);\n",
"\n",
"@show length(sol.t)"
]
},
{
"cell_type": "code",
"execution_count": 195,
"id": "5f38dcba-b033-4110-b36b-319c28b22dfe",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T16:02:52.537000+01:00",
"iopub.status.busy": "2022-01-28T16:02:52.537000+01:00",
"iopub.status.idle": "2022-01-28T16:02:52.729000+01:00",
"shell.execute_reply": "2022-01-28T16:02:52.729000+01:00"
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"Figure(PyObject <Figure size 640x480 with 1 Axes>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for k in 1:p[2]\n",
" plot(getindex.(sol.u, (k-1)*p[1] + 1), getindex.(sol.u, (k-1)*p[1] + 2), label = \"M$k\")\n",
"end\n",
"legend();"
]
},
{
"cell_type": "code",
"execution_count": 199,
"id": "a7c5747b-d722-48b1-9a6d-5d44d925f661",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T16:05:26.123000+01:00",
"iopub.status.busy": "2022-01-28T16:05:26.122000+01:00",
"iopub.status.idle": "2022-01-28T16:05:26.662000+01:00",
"shell.execute_reply": "2022-01-28T16:05:26.662000+01:00"
}
},
"outputs": [
{
"data": {
"text/plain": [
"(k = 6, j = 8)"
]
},
"execution_count": 199,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n1, n2 = (k=6, j=8)"
]
},
{
"cell_type": "code",
"execution_count": 200,
"id": "418f30b6-4e81-431b-9127-dc64f0777dd8",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T16:05:29.954000+01:00",
"iopub.status.busy": "2022-01-28T16:05:29.953000+01:00",
"iopub.status.idle": "2022-01-28T16:05:29.955000+01:00",
"shell.execute_reply": "2022-01-28T16:05:29.955000+01:00"
}
},
"outputs": [
{
"data": {
"text/plain": [
"6"
]
},
"execution_count": 200,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n1"
]
},
{
"cell_type": "code",
"execution_count": 201,
"id": "bbce375a-51ca-4f18-a061-4ab9ec6bc0e0",
"metadata": {
"execution": {
"iopub.execute_input": "2022-01-28T16:05:32.980000+01:00",
"iopub.status.busy": "2022-01-28T16:05:32.980000+01:00",
"iopub.status.idle": "2022-01-28T16:05:32.982000+01:00",
"shell.execute_reply": "2022-01-28T16:05:32.982000+01:00"
}
},
"outputs": [
{
"data": {
"text/plain": [
"8"
]
},
"execution_count": 201,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n2"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "48b648f4-d3b0-4744-8013-cccd38fb643d",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia (4 threads) 1.7.1",
"language": "julia",
"name": "julia-4threads-1.7"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.7.1"
}
},
"nbformat": 4,
"nbformat_minor": 5
}