{
"cells": [
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"from daomath.daomechanics import VectorField\n",
"from daomath.daomechanics import MaterialPoint\n",
"from daomath.ground import Ground\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import animation, rc\n",
"from IPython.display import HTML\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Physics Engine Implementation "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### AUTHOR : David Stankov"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ABSTRACT \n",
" Solving of the system non-linear differential equations using LeapFrog algorithm.So we will able to to calculate the body's motion according second principle of mechanics We will visualize the motions by Python lib pyplot,thus we will attain more understanding of what is vector field ,the innitial values ploblems and so on.In addition we will show the law of conservation of energy"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### INTRODUCTION\n",
"The priciple of meachanics defined by Nuton,help up to calculate and predict the motion of body when we known the force wich act on it and its inition values of velosaty and radius vector"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Vector Field \n",
"Vector field in two dimensions is a function that assigns to each point (x,y) of the xy-plane a two-dimensional vector F(x,y). The standard notation is $$\\vec{F}(x,y) = V(x,y).\\vec{i} + Q(x,y).\\vec{j} $$ \n",
" \n",
"The most famous example is force on Earh'surface $$\\vec{G}(x,y) = 0.\\vec{i} -g.\\vec{j}$$. where $$ g=9.8(\\frac{m}{s^2}) $$ found by Galileo Galilei. \n",
"Let's visualise this vector field using 'matplotlib.pyplot' and Vector Field where its implementation can be found in folder daomath\\mechanics in project\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"f = VectorField(lambda t,x,y : 0 , lambda t,x,y : -9.8)\n",
"f.plot_field(reduce=8,scale=10,width=0.003,label=r'$\\vec{g}$')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Other Field : $$\\vec{F}(x,y) = -x.\\vec{i} -y.\\vec{j}$$ : "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"\n",
"f = VectorField(lambda t,x,y : -x , lambda t,x,y : -y)\n",
"f.plot_field(reduce=4,scale=10,width=0.003)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Second principle of mechanics : \n",
" $$1) \\frac{d\\vec{p}}{dt} = \\frac{m.d^2\\vec{r(t)}}{dt^2}=\\frac{m.\\vec{dv}(t,\\vec{r})}{dt}=\\frac{m.\\vec{a}(t,\\vec{r})}{dt}=\\vec{F}(\\vec{r},t)$$ \n",
" where $$\\vec{r}(radious-vector),\\vec{a}(accelaration),\\vec{v}(velosity),\\vec{F}(force) \\in E^3 $$ E-euclidian vector space is radious .The low can be difined as $$$$ \n",
" In an inertial frame of reference, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma.\n",
"The equation 1) is six order system ODE.For solution of the equations we will use Leapfrog integration ,because the algorithms is more stable than Euler's method especially in oscillatory motion"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" The motion of the body on wich acts $$\\vec{F}(x,y) = 0.\\vec{i} -g.\\vec{j}$$ and\n",
"Initial Velocity is $$ \\vec{v_0} = 20.cos(45^{\\circ})\\vec{i} +cos (sin^{\\circ})\\vec{j} $$ \n",
"\n",
"The solving of differcial eqation is verry simple $$\\int{\\vec{v}dt} = \\int{0.dt}.\\vec{i} -\\int{g.dt}.\\vec{j} + \\int{\\vec{v_0}dt} = 20.cos45^{\\circ}.\\vec{i} + (20.sin45^{\\circ}-g.t).\\vec{j} $$\n",
"$$ \\int{d\\vec{r}(t)} = \\int{\\vec{v}dt} =20.sin45^{\\circ}.t.\\vec{i} + (20.cos45^{\\circ}-g).t^2.\\vec{j} + \\vec{r_0}$$\n",
"Let's visualise this motion"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"17\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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MHg1Ll/o3mFnsNFIq9t8fevf21Tw/+yx2mtKmQk+JL77w8cyDD4aePWOnkVLzq1/B++/DzTfHTlLaVOgpcdttsGyZjs4ljgMP9AOJESO0VV1MKvQUWLvWT0oddBB06xY7jZSqK6+Eigr4299iJyldKvQUGDfOx86vuEJH5xLPwQdD9+7wxz9qXnosKvSEW78e/t//g/328xNTIjFdeSW8+y7cckvsJKVJhZ5wEybAokVw+eU6Opf4unaFww/3IcDVq2OnKT0q9ATbsMFntuy5Jxx7bOw0Iu7KK/3q0dGjYycpPSr0BJs2DV56ybeY01WhUiwOO8xP0I8Y4QvFSeGoBhIqBD86b98ejj8+dhqRr5jBpZf6Sozjx8dOU1pU6Ak1ezbMm+ffOPXrx04j8nX9+kHHjnDNNdp7tJBU6Al19dXQujUMHRo7ici3bbaZbyS9YAFMnx47TelQoSfQ00/DI4/AxRdDw4ax04hs2gknwE47+VG6FIYKPYFGjIDtttNeoVLcGjTwg47HH/c/kn8q9IRZvBjuvRfOPhu22ip2GpHvNnw4NGvm89Il/1ToCXP99X7kc955sZOIVK9xYzj//K+m2Ep+qdATpKLCV1U85RRo2TJ2GpHsnHsubLklXHtt7CTpp0JPkJtv9nXPL7oodhKR7DVt6ud77roL3n47dpp0U6EnxKpVvhFvv35+qb9Ikpx/vi9Voc2k80uFnhBjx8J778Ell8ROIlJz7dv7ekN//7s2wMgnFXoCrF/v+zV26eKr2Ykk0YUXwocfwpgxsZOklwo9ASZP9umKF1+sJXIluQ46CA44AG64wYdfJPdU6Alw3XXQrh0MHBg7iUjtmflR+uLFPo1Rck+FXuSeeQaefBIuuADq1YudRqRuBg705QCuvz52knTKutDNrJ6ZPWdm0zL325nZXDNbZGbjzWzz/MUsXTfdBFtvDaeeGjuJSN3Vr+8HJ488AvPnx06TPjU5Qr8AeHWj+38AbgghdAA+BIbnMpjAO+/4etKnngrbbBM7jUhuDB/uy1bccEPsJOmTVaGbWRugLzAqc9+AbsCEzFPGAMfkI2Ap+/vffccXXeYvabLttn6h0fjxsGxZ7DTpku0R+o3Az4DKc9PbAx+FECo3mFoGtM5xtpL25ZcwciT06QMdOsROI5JblRca/fWvsZOkS7WFbmb9gJUhhI1HvDY1eW6T+5KY2ZlmVm5m5RUVFbWMWXrGj4eVK328USRt2rWD/v1h1ChfzkJyI5sj9EOA/mb2JnAXPtRyI9DEzCo3P2sDLN/UXw4h3BJCKAshlDVv3jwHkdMvBD8ZuueecOSRsdOI5Md55/nVz3ffHTtJelRb6CGEX4QQ2oQQ2gLHAw+GEE4CHgIGZZ42DJict5Ql5sknfQbA+efrQiJJr27dYI894M9/1r6juVKXeeg/By40s8X4mPqtuYkkf/oTNGniy+SKpJWZH6WXl/uG51J3NSr0EMLDIYR+ma+XhBC6hBB2DSEMDiF8mZ+IpeWtt3xHotNP9zWkRdJs6FC/zkKrMOaGrhQtMiNH+q+fmqoopWDrreHHP/Zx9HffjZ0m+VToReTLL/2s/9FHw847x04jUhjnnANr1vi/fakbFXoRufde32bu7LNjJxEpnD32gB49/LfTdeuqf75UTYVeREaOhF128X/cIqXkvPN8e7rJmitXJyr0IvHSS/DYY3DWWbCZPhUpMX37Qtu2OjlaV6qOIvG3v0HDhlpVUUpTvXo+lv7ww7BgQew0yaVCLwKffQb//CcMGQLNmsVOIxLHaafB5pv7onRSOyr0IjBuHHz6qU6GSmnbfnsYNMgPblatip0mmVTokYUAN98M++wDBx4YO41IXGedBR9/7IvTSc2p0CN76il48UU/Ote6LVLqunb1Rek07FI7KvTIRo70q+VOOil2EpH4zODMM2HuXHjhhdhpkkeFHlHl0qFDh/qWXCLi3w8NG+oovTZU6BGNGeOXPP/kJ7GTiBSPpk19xte//uUzwCR7KvRIQvC1Kw46CDp1ip1GpLicdZbP/LrrrthJkkWFHsmTT8LChb5Mroh83cEHw157adilplTokfzjHz5uPmRI7CQixcfMj9LLy+HZZ2OnSQ4VegQff+wnQ088USdDRapyyinQqJGO0mtChR7BnXfC6tUabhH5Lk2awHHHwR136ORotlToEYwaBXvvDWVlsZOIFLczzvAyv+ee2EmSQYVeYM89B/Pn+9G5rgwV+W4HHQS77w6jR8dOkgwq9AIbNcovmjj55NhJRIqfGQwfDo8/Dq+9FjtN8VOhF9CqVb6y4qBBsN12sdOIJMMpp/h66bfdFjtJ8VOhF9DEiT7DRSdDRbL3ve/5jkZjxmjP0eqo0Ato1CjYdVc47LDYSUSS5bTTYMUKuP/+2EmKmwq9QBYtgkcf9fFAnQwVqZk+faBFC50crY4KvUDGjPHNn4cOjZ1EJHkaNPDvnalTYeXK2GmKlwq9ADZsgLFjoWdPaNUqdhqRZDr1VB9D/+c/YycpXir0AnjoIXjrLfjxj2MnEUmuPff0eemjR/tqpfJtKvQCuP122HZbGDAgdhKRZDvtNHjlFZg3L3aS4qRCz7NPPvHpiscfD1tsETuNSLINGQKNG8Ott8ZOUpxU6Hk2YYIvxKXhFpG622YbvzBv/Hj/vpKvU6Hn2e23w267wQEHxE4ikg7DhvlvvlOmxE5SfFToefTGG/DYY350rrnnIrlx+OHQpo1mu2yKCj2Pxo71Ij/llNhJRNJjs818cbv774d3342dprio0PNkwwa/mOjII/1oQkRy55RTYP163yxGvqJCz5NHH4WlS3UyVCQfOnaEH/xAwy7fpELPk9tvh623hmOOiZ1EJJ2GDvUNpBcsiJ2keKjQ8+Czz3y64nHH+ZxZEcm944+H+vV1lL4xFXoe3HsvfP65T68SkfzYYQfo1Qv+9S8fT5csCt3MtjCzeWb2gpm9bGZXZR5vZ2ZzzWyRmY03s83zHzcZxo2Ddu3gkENiJxFJt6FDYflyXy9JsjtC/xLoFkLYB9gX6GVmBwJ/AG4IIXQAPgSG5y9mcqxYAbNnw4knau65SL4dfbSvkzR2bOwkxaHaQg/us8zdBpk/AegGTMg8PgbQ6T/8kuQNG+Ckk2InEUm/Lbbw9V0mTvRzV6UuqzF0M6tnZs8DK4FZwBvARyGEyh3+lgGt8xMxWcaNg/3286U+RST/hg71Ddj//e/YSeLLqtBDCOtDCPsCbYAuwKbqapMrFJvZmWZWbmblFRUVtU+aAK+/Ds88o6NzkUI65BA/Z6VhlxrOcgkhfAQ8DBwINDGz+pn/1AZYXsXfuSWEUBZCKGvevHldsha9ceN83Pz442MnESkdlctrzJkDb78dO01c2cxyaW5mTTJfNwKOBF4FHgIGZZ42DJicr5BJEIIX+hFHQGsNPokU1Ikn+vfg3XfHThJXNkfoLYGHzOxF4BlgVghhGvBz4EIzWwxsD5T0kvPz5vnqiiefHDuJSOnZfXfo3Flru9Sv7gkhhBeB/Tbx+BJ8PF3wo/OGDWHgwNhJRErTCSfAJZfAokXQoUPsNHHoStEcWLfOpytWzokVkcI7/ngfT7/rrthJ4lGh58Ds2bBypWa3iMTUpg107Qp33OHj6aVIhZ4D48ZBkybQu3fsJCKl7YQTYOFCeOGF2EniUKHX0eef+wUNgwf7GLqIxDNokK/AWKonR1XodTRlipe6hltE4mvWDHr29ELfsCF2msJTodfRnXd+NXYnIvGdeCK89RY8+WTsJIWnQq+Djz7yjWqHDPGNa0UkvgEDoFGj0hx2UQ3VwaRJsHat70wkIsVhq62gf3+/anTt2thpCkuFXgfjx/uiQPvvHzuJiGzshBPgvfd8fZdSokKvpfff9/nnQ4ZoIwuRYtOrl08lvuOO2EkKS4VeS/fe61eIarhFpPg0bAg/+pFPKV69OnaawlGh19L48b5exL77xk4iIptywgm+i9H06bGTFI4KvRbefdc3pT3uOA23iBSrww6D5s3hnntiJykcFXotTJjgFy1ouEWkeNWv78MuU6f6FnWlQIVeC+PHQ8eO0KlT7CQi8l0GD/YynzEjdpLCUKHX0Ntvw+OP6+hcJAkOPRR22KF0djJSodfQPff40pwqdJHiV7++bzozbVppDLuo0Gto/HjYZx/f8kpEit+QIV7mpTDbRYVeA0uXwtNP6+hcJEkqh11KYbaLCr0GKsfhVOgiyVGvns92mTbNl7pOMxV6Ddx9N5SVQfv2sZOISE1UznZJ+7CLCj1Lb74J5eX+D0NEkqVUhl1U6Fm6916//dGP4uYQkZorlWEXFXqWJk702S277BI7iYjUxpAhvlBXmoddVOhZePtt385q0KDYSUSktrp2hRYt0n2RkQo9C//+t99quEUkuSqHXe67L73DLir0LEycCHvu6X9EJLkGD/Zhl/vui50kP1To1Vi5Eh59VMMtImnQtavPdqmc5JA2KvRqTJrkS+VquEUk+erVg2OO8SP0L76InSb3VOjVmDjRZ7bsvXfsJCKSCwMH+k5Gs2fHTpJ7KvTv8MEH8OCDPtyinYlE0uGII2DbbdM57KJC/w5TpvhG0BpuEUmPzTeHo4+GyZP9+ztNVOjfYeJE2GknX79FRNJj4ED/DfzRR2MnyS0VehU++QQeeMCPzjXcIpIuRx0FjRqlb9hFhV6FadNgzRoNt4ikUePG0Lu3XzS4YUPsNLmjQq/CxInQsiUcdFDsJCKSDwMHwvLlMG9e7CS5o0LfhMpdwo89FjbT/0MiqdS3r+85Wrm0RxqorjbhgQf88uCBA2MnEZF8adIEunf3cfQQYqfJjWoL3cx2NLOHzOxVM3vZzC7IPN7UzGaZ2aLM7Xb5j1sYkyf7h33oobGTiEg+DRwIixfDggWxk+RGNkfo64CLQgh7AgcC55pZR+BSYE4IoQMwJ3M/8datg6lT/dexBg1ipxGRfBowwGexpWW2S7WFHkJ4J4TwbObrT4FXgdbAAGBM5mljgGPyFbKQnngC3n/f13sQkXRr0QJ++MMSKvSNmVlbYD9gLtAihPAOeOkDO+Q6XAyTJkHDhj5PVUTSb+BAePFFH3pJuqwL3cy2AiYC/xtC+KQGf+9MMys3s/KKioraZCyYELzQjzwStt46dhoRKYRjj/XbNMx2yarQzawBXubjQgiVv5y8a2YtM/+9JbByU383hHBLCKEshFDWvHnzXGTOm5degjff1HCLSCnZeWfo3LlECt3MDLgVeDWEcP1G/2kKMCzz9TBgcu7jFdakSX6C5OijYycRkUIaMACefhrefTd2krrJ5gj9EOAUoJuZPZ/50we4BuhhZouAHpn7iTZpkl8Z2qJF7CQiUkgDBviQ67RpsZPUTf3qnhBCeByoanmq7rmNE8/SpfDcc3DttbGTiEih7b23D71MmQLDh8dOU3u6UjRjcmbASOPnIqXHDPr3h1mzfOmPpFKhZ0yaBB07QocOsZOISAz9+/uSH0nemk6FzlcL3Q8YEDuJiMRy2GG+Nd3kBE/vUKHjO4CvX6/hFpFS1qCBr5E+dar3QRKp0PHhllattNWcSKkbMAAqKmDu3NhJaqfkC331arj/fv8gtfa5SGnr1cvXSJ8yJXaS2in5Cps9289qa7hFRJo0gcMPT+44eskX+uTJsM02/iGKiPTvDwsXwuuvx05ScyVd6Bs2+JVhvXrB5pvHTiMixaB/f79N4rBLSRf6/Pm+doPWbhGRSjvvDPvso0JPnKlT/URor16xk4hIMenf3ze7ee+92ElqpqQLfdo0X4yrWbPYSUSkmAwY4EOy990XO0nNlGyhv/22L8al4RYR+abOnaF16+TNdinZQq9cJrNfv7g5RKT4VC7WNXMmfPFF7DTZK+lCb9fOF+QSEfmm/v39GpU5c2InyV5JFvqqVX5BUb9+/pNYROSbjjgCttwyWePoJVnoDz7ov0Zp/FxEqtKwoW8Yf999vptREpRkoU+bBlttBYceGjuJiBSzvn3hv/+Fl1+OnSQ7JVfolfsGHnWU/wQWEalKnz5+m5S9Rkuu0J9/3qcsanaLiFSndWvYb7/kjKOXXKFPm+YnQit/8oqIfJe+feHJJ31ns2JXcoWNB4o2AAAMV0lEQVQ+dSoccADssEPsJCKSBH37+lWjM2fGTlK9kir0FSvgmWc03CIi2dt/f18eJAnDLiVV6JUfiKYriki26tXzIdoZM4p/r9GSKvRp02DHHeH734+dRESSpG9fH0N/+unYSb5byRT6F1/ArFl+dK6rQ0WkJnr29CP1Yh92KZlCf+QR+Pxz/0krIlITTZrAD3+oQi8a06fDFlv4+gwiIjXVty+8+CK89VbsJFUrmUKfMQO6dYNGjWInEZEkqpwdV8xH6SVR6IsXw6JF0Lt37CQiklR77OFLbqvQI5sxw29V6CJSW2Y+7DJnDqxeHTvNppVMoe+2G+yyS+wkIpJkfft6mT/8cOwkm5b6Ql+9Gh56SEfnIlJ3hx8OjRsX77BL6gv94Yd9DroKXUTqaostfNOLadOKc9OL1Bf6jBk+s+Www2InEZE06NMHli6F116LneTbUl/o06f7dMUttoidRETSoFcvv62cbFFMUl3oixbBG29ouEVEcmfnnWHPPeH++2Mn+bZUF7qmK4pIPvTq5cuJrFoVO8nXpbrQp0+H3XeH9u1jJxGRNOnVC7780ku9mFRb6GY22sxWmtmCjR5ramazzGxR5na7/MasuVWrfIaLjs5FJNcOPdQnWxTbOHo2R+i3A72+8dilwJwQQgdgTuZ+UXnoIf8JqkIXkVyrXOiv2MbRqy30EMKjwDe3Rx0AjMl8PQY4Jse56mzGDL8A4NBDYycRkTTq1euriRfForZj6C1CCO8AZG6r3HLZzM40s3IzK6+oqKjly9VMCF+trqjpiiKSD5XTF4tp8+i8nxQNIdwSQigLIZQ1b9483y8HwOuvw5IlGm4RkfzZdVefcFFMwy61LfR3zawlQOZ2Ze4i1Z2mK4pIvpl5xzz4oJ+vKwa1LfQpwLDM18OAybmJkxszZny1drGISL706uVbWz7+eOwkLptpi3cCTwG7m9kyMxsOXAP0MLNFQI/M/aKwapXPDdXRuYjk2+GHw+abF8+wS/3qnhBCOKGK/9Q9x1ly4tFH/defo46KnURE0m6rraBrVy/0P/4xdpoUXin6wAPQsKH/nywikm+9e8OCBcWxeXTqCn3mTJ973rhx7CQiUgqKafpiqgp92TJ45RXo2TN2EhEpFR07Qps2xTGOnqpCf+ABv9X4uYgUipkfpc+aBWvXxs2SukJv2RI6dYqdRERKSe/e8Mkn8PTTcXOkptDXr/efkD17+k9MEZFC6d4d6tWLv/piagr92Wfhgw80fi4ihbfttnDQQX5QGVNqCr1y/PzII+PmEJHS1KMHzJ8P778fL0NqCn3mTOjcGXaoct1HEZH86dnTV3qdMydehlQU+iefwFNPabhFROIpK/Ohl8rRghhSUegPPQTr1mm6oojEU7++nxydNcuP1GNIRaE/8ABsuSUcfHDsJCJSynr0gP/+13cyiiE1hX7EEb7qmYhILD16+G2sYZfEF/qSJbB4scbPRSS+XXbxXYxiTV9MfKFX/iRUoYtIMejRw8/rxVgGIPGFPnMm7Lwz7LZb7CQiIn5w+emnMHdu4V870YW+dq3v56fL/UWkWHTrBpttFmfYJdGFPneuz0HXdEURKRZNmsD++8c5MZroQn/gAf9J2K1b7CQiIl/p2RPmzYOPPirs6ya60GfP9p+E220XO4mIyFd69IANG3xIuJASW+gff+w/AbUYl4gUmwMP9A2kCz2OnthCf+QRXwNdhS4ixaZBA7/YsdDj6Ikt9DlzoFEjX4NYRKTY9OjhFz4uWVK410xsoc+eDV27QsOGsZOIiHxb5cWOhRx2SWShL18Or7yi4RYRKV677QY77ljYYZdEFnrlAvIqdBEpVmZ+lP7gg768dyEkttC33x722Sd2EhGRqvXo4XPRy8sL83qJK/QQfPy88vJaEZFi1b27386eXZjXS1wlvvYavP22hltEpPg1awb77adCr1Ll/zEqdBFJgiOP9D2PP/88/6+VuEKfMwfatvVF5EVEit2RR0KLFvCf/+T/tern/yVyZ906Xzh+8ODYSUREsnPkkbB0aWGW+E5Uoc+f72u4aLhFRJKikJM3EjXkUjn/XMvlioh8W6IKffZsn3vevHnsJCIixScxhb5qFTzxhIZbRESqkphCf/xxWLNGhS4iUpWiLvQlS5Zwzjnn0Lp1a4466lpgDRMn/i9LCrkepYhIQtSp0M2sl5m9ZmaLzezSXIUCmD59Op06dWLkyJEsX74c6A48xahRf6JTp05Mnz49ly8nIpJ4tS50M6sH/BXoDXQETjCzjrkItWTJEgYNGsTq1aszj2wP7Af4ZaKrV69m0KBBOlIXEdlIXY7QuwCLQwhLQghrgLuAAbkINWLEiI3KHOAIPOqc/3tk9erVjBgxIhcvJyKSCnUp9NbAWxvdX5Z5rM4mT578jUe6A58Az1TzPBGR0lWXQt/UhazhW08yO9PMys2svKKiIqv/4XfeeecbjywBRgNfXyV+xYoV2SUVESkBdSn0ZcCOG91vAyz/5pNCCLeEEMpCCGXNs7wiqGXLlt945I/AT7/1vO9973tZhxURSbu6FPozQAcza2dmmwPHA1NyEWrAgOyG4rN9nohIKah1oYcQ1gHnATOBV4G7Qwgv5yLUxRdfTKNGjb7zOY0aNeKSSy7JxcuJiKRCneahhxCmhxB2CyHsEkK4Oleh2rdvz4QJE6os9UaNGjFhwgTatWuXq5cUEUm8or1StE+fPixYsICzzz6bVq1asdlmm9GqVSvOPvtsXn75Zfr06RM7oohIUbEQvjUxJW/KyspCeaG2vxYRSQkzmx9CKKvueUV7hC4iIjWjQhcRSQkVuohISqjQRURSQoUuIpISKnQRkZRQoYuIpIQKXUQkJQp6YZGZVQBLa/nXmwHv5TBOUpTi+y7F9wyl+b71nrOzcwih2uVqC1rodWFm5dlcKZU2pfi+S/E9Q2m+b73n3NKQi4hISqjQRURSIkmFfkvsAJGU4vsuxfcMpfm+9Z5zKDFj6CIi8t2SdIQuIiLfIRGFbma9zOw1M1tsZpfGzpMPZrajmT1kZq+a2ctmdkHm8aZmNsvMFmVut4udNdfMrJ6ZPWdm0zL325nZ3Mx7Hp/ZszZVzKyJmU0ws4WZz/ygtH/WZvbTzL/tBWZ2p5ltkcbP2sxGm9lKM1uw0WOb/GzN3ZTpthfNrHNdXrvoC93M6gF/BXoDHYETzKxj3FR5sQ64KISwJ3AgcG7mfV4KzAkhdADmZO6nzQX4vrSV/gDckHnPHwLDo6TKrz8B94cQ9gD2wd9/aj9rM2sNnA+UhRA6AfXwjeXT+FnfDvT6xmNVfba9gQ6ZP2cCI+vywkVf6EAXYHEIYUkIYQ1wFzAgcqacCyG8E0J4NvP1p/g3eGv8vY7JPG0McEychPlhZm2AvsCozH0DugETMk9J43veBjgUuBUghLAmhPARKf+sgfpAIzOrDzQG3iGFn3UI4VHgg288XNVnOwAYG9zTQBMza1nb105CobcG3tro/rLMY6llZm2B/YC5QIsQwjvgpQ/sEC9ZXtwI/AzYkLm/PfBRCGFd5n4aP+/2QAVwW2aoaZSZbUmKP+sQwtvACOC/eJF/DMwn/Z91pao+25z2WxIK3TbxWGqn5pjZVsBE4H9DCJ/EzpNPZtYPWBlCmL/xw5t4ato+7/pAZ2BkCGE/4HNSNLyyKZkx4wFAO6AVsCU+3PBNafusq5PTf+9JKPRlwI4b3W8DLI+UJa/MrAFe5uNCCPdmHn638lewzO3KWPny4BCgv5m9iQ+ldcOP2Jtkfi2HdH7ey4BlIYS5mfsT8IJP82d9JPCfEEJFCGEtcC9wMOn/rCtV9dnmtN+SUOjPAB0yZ8M3x0+kTImcKecyY8e3Aq+GEK7f6D9NAYZlvh4GTC50tnwJIfwihNAmhNAW/1wfDCGcBDwEDMo8LVXvGSCEsAJ4y8x2zzzUHXiFFH/W+FDLgWbWOPNvvfI9p/qz3khVn+0UYGhmtsuBwMeVQzO1EkIo+j9AH+B14A3g8th58vQef4j/qvUi8HzmTx98THkOsChz2zR21jy9/8OBaZmv2wPzgMXAPUDD2Pny8H73Bcozn/ckYLu0f9bAVcBCYAHwT6BhGj9r4E78PMFa/Ah8eFWfLT7k8tdMt72EzwKq9WvrSlERkZRIwpCLiIhkQYUuIpISKnQRkZRQoYuIpIQKXUQkJVToIiIpoUIXEUkJFbqISEr8f6aUIA8oFApCAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(6, 6))\n",
"fig = plt.figure(figsize=(6, 6))\n",
"\n",
"u = lambda t, x, y: 0\n",
"v = lambda t, x, y: -10\n",
"point = MaterialPoint(x0=0, y0=0, mass=1)\n",
"f = VectorField(u, v)\n",
"point.add_force(f)\n",
"z = point.calculate_radius_vector(20*np.cos(np.pi/4), +50*np.sin(np.pi/4),n=700)\n",
"plt.plot(z[:,0],z[:,1])\n",
"size = int(point.get_size(40))\n",
"print(size)\n",
"\n",
"\n",
"\n",
"anim = animation.FuncAnimation(plt.gcf(), point.update_HTML_animation,interval=100,fargs=(fig,),frames=size, blit=False)\n",
"HTML(anim.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"let's to see radius vector"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"\n",
"plt.plot(z[:,0],z[:,1])\n",
"\n",
"point.plot_radios_vector()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"if we change the the initial velosity for exampe (0,50) we will see"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(6, 6))\n",
"fig = plt.figure(figsize=(6, 6))\n",
"z = point.calculate_radius_vector(0, 50,n=1000)\n",
"plt.plot(z[:,0],z[:,1])\n",
"size = int(point.get_size(20))\n",
"anim = animation.FuncAnimation(plt.gcf(), point.update_HTML_animation,interval=100,fargs=(fig,),frames=size, blit=False)\n",
"HTML(anim.to_html5_video())"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(6, 6))\n",
"fig = plt.figure(figsize=(6, 6))\n",
"z = point.calculate_radius_vector(10, 70,n=1000)\n",
"plt.plot(z[:,0],z[:,1])\n",
"size = int(point.get_size(20))\n",
"anim = animation.FuncAnimation(plt.gcf(), point.update_HTML_animation,interval=100,fargs=(fig,),frames=size, blit=False)\n",
"HTML(anim.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"Gravity $$\\vec{G}= - \\frac{M.m.x}{(x^2+y^2)^{3/2}}\\vec{i} -\\frac{M.m.y}{(x^2+y^2)^{3/2}}\\vec{j} $$ Where F is the force, m1 and m2 are the masses of the objects interacting,we will consider the equation in more simplified\n",
" case where the M is times greater then m is with initial values $$ x_0= 10 , y_0 =10, v_1 = -1.cos45^{\\circ}, v_2 = -4.sin45^{\\circ}$$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(6, 6))\n",
"point = MaterialPoint(x0=10,y0=10)\n",
"# z = point.calculate_radius_vector(3,4)\n",
"# anim = animation.FuncAnimation(fig, point.update_HTML_animation, fargs=(Q, X, Y),\n",
"# interval=50, blit=False)\n",
"u = lambda t, x, y: -80 * x / ((x ** 2 + y ** 2) ** (3 / 2))\n",
"v = lambda t, x, y: -80 * y / ((x ** 2 + y ** 2) ** (3 / 2))\n",
"point = MaterialPoint(x0=7, y0=7, mass=1)\n",
"f = VectorField(u, v)\n",
"point.add_force(f)\n",
"z = point.calculate_radius_vector(-1*np.cos(np.pi/4), -4*np.sin(np.pi/4),5000,h=0.005)\n",
"plt.plot(z[:,0],z[:,1])\n",
"size = int(point.get_size(100))\n",
"anim = animation.FuncAnimation(fig, point.update_HTML_animation,interval=50,fargs=(fig,),frames=size, blit=False)\n",
"HTML(anim.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"we can notice that the velocity near to center (0,0) is most fast\n",
"if we change $$ v_1=-10.cos45^{\\circ}, v_2 = -5.sin45^{\\circ}$$"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(6, 6))\n",
"point = MaterialPoint(x0=10,y0=10)\n",
"# z = point.calculate_radius_vector(3,4)\n",
"# anim = animation.FuncAnimation(fig, point.update_HTML_animation, fargs=(Q, X, Y),\n",
"# interval=50, blit=False)\n",
"u = lambda t, x, y: -80 * x / ((x ** 2 + y ** 2) ** (3 / 2))\n",
"v = lambda t, x, y: -80 * y / ((x ** 2 + y ** 2) ** (3 / 2))\n",
"point = MaterialPoint(x0=7, y0=7, mass=1)\n",
"f = VectorField(u, v)\n",
"point.add_force(f)\n",
"z = point.calculate_radius_vector(-10*np.cos(np.pi/4), -5*np.sin(np.pi/4),n=1000,h=0.003)\n",
"plt.plot(z[:,0],z[:,1])\n",
"size = int(point.get_size(100))\n",
"anim = animation.FuncAnimation(fig, point.update_HTML_animation,interval=50,fargs=(fig,),frames=size, blit=False)\n",
"HTML(anim.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"we can notice that the body is gone to out of orbit and just passed near to source of gravity .because the force is not strong enought to change the initial velocity. \n",
"In the last example will be shown how the stability of LeapFrog integration , when we change the intergration step h = 0.5 "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(6, 6))\n",
"point = MaterialPoint(x0=10,y0=10)\n",
"# z = point.calculate_radius_vector(3,4)\n",
"# anim = animation.FuncAnimation(fig, point.update_HTML_animation, fargs=(Q, X, Y),\n",
"# interval=50, blit=False)\n",
"u = lambda t, x, y: -80 * x / ((x ** 2 + y ** 2) ** (3 / 2))\n",
"v = lambda t, x, y: -80 * y / ((x ** 2 + y ** 2) ** (3 / 2))\n",
"point = MaterialPoint(x0=10, y0=10, mass=1)\n",
"f = VectorField(u, v)\n",
"point.add_force(f)\n",
"z = point.calculate_radius_vector(-1*np.cos(np.pi/4), -4*np.sin(np.pi/4),7000,h=0.5)\n",
"plt.plot(z[:,0],z[:,1])\n",
"size = int(point.get_size(100))\n",
"anim = animation.FuncAnimation(fig, point.update_HTML_animation,interval=50,fargs=(fig,),frames=size, blit=False)\n",
"HTML(anim.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wow!!! \n",
"We've attain the entirely different result.\n",
"The error growth factor is increased when the integration factor also increase . After many oscillation this error become enormous"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Work ,Energy and Potencial Field"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"Work is the product of force and distance. In physics, a force is said to do work if, when acting, there is a movement of the point of application in the direction of the force.\n",
"For example, when a ball is held above the ground and then dropped, the work done on the ball as it falls is equal to the weight of the ball. \n",
"The work of system by definition is integral of dW where $$ dW = \\vec{F}.d\\vec{r} = m.\\vec{a}.d\\vec{r}$$\n",
"###### \n",
"1) $$\\vec{F}.d\\vec{r} = m.\\vec{a}.d\\vec{r}=m.\\frac{\\vec{v}} {dt}.\\vec{v}.dt=m.\\vec{v}.d\\vec{v}$$\n",
"2) from 1 we have $$\\vec{F}.d\\vec{r}=m.\\vec{v}.d\\vec{v} \\Leftrightarrow \\int m.\\vec{F}.d\\vec{r} =\\int m.\\vec{v}.d\\vec{v} \\Leftrightarrow \\frac{m.v^2}{2} - \\frac{m.v_0^2}{2} = V(\\vec{r}) - V_0(\\vec{r}) \\Leftrightarrow \\triangle T = \\triangle V $$ \n",
"\n",
"T is kinetic V potential energy $$E + U = H$$ H is called total energy of system also Hamilton \n",
"$$grad\\vec{F}=\\vec{\\triangledown}.U = \\vec{F}$$\n",
"\n",
"accordingly theorem of Green if $$ \\int_C \\vec{\\triangledown} \\times \\vec{F}=0$$ then then the vector field is potential and satisfy $$grad\\vec{F}=\\vec{\\triangledown}.U = \\vec{F}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Law of conversations\n",
"For the first time in above example,we've saw the low of conservation .How does kinetic energy is transformed to potential energy and inverse process is the same .The most famous example is gravity on earth's surface: \n",
"$$m.g.y - m.g.y_o = E - E_0 \\Leftrightarrow E = H - m.g.y$$\n",
"\n",
"There are many kinds of transformation of energy ,maybe that is the most deeply and fundamental law in physics.\n",
"Let's see other kind of conversation - The Law of Momentum Conservation\n",
"Consider a collision between two objects.-obeject 1 and object 2 \n",
"Newton's third law says the force in moment of collision between obj1 and obj2 is equal in their magnitude and opposite in their direction\n",
"$$ 1)\\vec{F_{12}} = - \\vec{F_{21}}$$ \n",
"\n",
"let's multiple equation 1) with dt and after that we can integrate it $$\\vec{F_{12}} = - \\vec{F_{21}} $$\n",
" $$\\vec{F_{12}}.dt = - \\vec{F_{21}}.dt \\Leftrightarrow m.\\vec{a_{12}}.dt -m.\\vec{a_{21}}.dt \\Leftrightarrow \\int m.\\vec{a_{1}}.dt =\\int m.\\vec{a_{2}}.dt = m.\\vec{v_{1}}.dt + m.\\vec{v_{2}} \\Leftrightarrow \\vec{p_{1}} + \\vec{p_{2}} =\\vec{p}$$\n",
"The conclusion from above operation is after collision the total momentum of system remains the sameThe conclusion from above operation is after collision the total momentum of system ramains the same \n",
"\n",
"Let see what 's happens with energy conversation:\n",
"After the multiplacation of eaqution 1) on both sides with $$\\vec{dr}$$ and integration we achieve the result\n",
"$$\\vec{F_{12}}.d\\vec{r} =-\\vec{F_{21}}.d\\vec{r} = T_{12} + T_{21} = H $$\n",
"The total energy between two particle remains the same.This result can be summarise for many particul"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's see visualization of collision between to body "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(6, 6))\n",
"fig = plt.figure(figsize=(6, 6))\n",
"g = Ground()\n",
"g.add_point(MaterialPoint(x0=0, y0=5, mass=5, v_x0=3, v_y0=0))\n",
"g.add_point(MaterialPoint(x0=10, y0=5, mass=15, v_x0=-3, v_y0=0))\n",
"\n",
"g.calculate_speed_points(end_time=80)\n",
"points = g.points\n",
"\n",
"size = len(g.points[0].x_args)\n",
"anim = animation.FuncAnimation(fig, g.update_HTML_animation,interval=80,fargs=(fig,),frames=size, blit=False)\n",
"HTML(anim.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"After the collion we can notice that the red ball is smaller velositt before colion,\n",
"because its mass greater than blue ball.\n",
"That fact comes from The fact $$H = E_1+E_2 , E_i=\\frac{H}{2} $$ and $$v =\\sqrt{ \\frac{E}{2*m}} $$ The more mass gives less velocity"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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PEOgA4AkCHQA8QaADgCcIdADwBIEOAJ4g0AHAEwQ6AHiCQAcATxDoANAD+1atUrC5OdZltEOgA0AP1FdX6/9dc41KXn5ZzrlYlyOJQAeAHhn/6U8rPiVFb3//+3r5hht0cOtWSVJFRYXWrFmj119/XWvWrFFFRUWv1RTuM0V7VXN1veqLDipY06RAWoKSc4YqPj051mUBOANZIKCP/eAHeu3WW1VbWakDjY16+ne/U2lpaYdts7KyNH/+fI0bNy66NfXmjwp5eXkuPz+/2/u1HG3UoaU7VLdpf4f3UqYO15CrJypuYGIkSgSAbilaskQ7N2xQ2Ztvau8ll6glKSnkdmamq666SjNmzOj2OcyswDl32uc39/khl5ajjap8ZGPIMJekuk37VfnIRrUcbezlygBASpozR6uSklQzapTGvPGG4hoaQm7nnNPzzz+vPXv2RK2WPh/oh5buUEt1vSQp6IJ6dccqPbjyCb26Y5WCLihJaqmu16GlO2JZJoAz1PLlyyUzHTjvvOOhvruwUG+++aaKioraTZg657Rs2bKo1dKnx9Cbq+uP98yDLqhvPfOveqX4nePvX549V4s+/0sFLKC69/erubqeMXUAvaaiouKjMXMz7Z8yRYVbtii3okJ/371bR1talJubq+uuu05mJkkqLS1VRUWFMjMzI15Pn+6h1xcdPP796ztX65Xid5QaCGhyaqok6ZXid/T6ztWtG7j22wNAtO3evbvd6+IdO/TI1q1aX1Ojy4cOlSRt27ZNxcXF7bYrKSmJSj19OtCDNU3Hv99UsV2SNDA+XneOGaPUQGvp71cUhdweAKKttra23evy8nJJ0lOVlfrH/v0d2j907NixqNTTpwM9kJZw/PupmedIkioaG7W+pkbz09MlSedl5oTcHgCiLbVttOBDo0aNOv6966RdkgYMGBCVevp0oCfnDD3+/byzZ+ny7LmSpGf379f89HR9Nnu25p09q3UDa789AETb+PHj273Ozs5Wbm5uu7bc3FxlZ2e3a4vWevQ+PSkan56slKnDVbdpvwIW0KLP/1Kv71yt9yuKNKC5QvdknquAtf6flHLecCZEAfSqzMxMZWVlHZ8YNTNdd911Ki4uVnl5uUaNGqXs7OzjE6JS60VG0ZgQlfp4D11S60VDbUEdsIAunThbd865SbNm3KSyD15Tc1Ot4tKTNeTqiTGuFMCZaP78+e1em5lycnJ08cUXKycnp12Ym5kWLFgQtVr6fKDHDUzUiDumKWXqcOmj3xelpGUqPXOqKo6t1og7pnGlKICYGDdunK6++up2wR3Kh1eKjh07Nmq19ItL/z908r1cmpKP6tVv36yrXnpJiYMGRbBSAOiePXv2aNmyZZ3ey2XBggU9DvOuXvrfrwI9lFU/+YnSxo7V1G9/O6LHBYCeqKioUElJiY4dO6YBAwZo3LhxYY+ZdzXQ+/SkaFdMuf12vXLjjcr96lfppQOIuczMzKhNep5Onx9DP51B48dr9MUXa9tf/hLrUgAgpvp9oEutvfTtTz6pxiNHYl0KAMSMF4F+Yi+9sqAg1uUAQEx4EejBpialjRun9x97TO8/+misywGAmPAi0AMJCUodOVKuuVmHi4pOvwMAeMiLQJekiZ/7nGbcc4/qqqrUcOhQrMsBgF7X75ctnmjS176mpqNHdaioSJkzZ8a6HADoVV4FuiSdd8cdajjIgy4AnHm8GXL5kJkpue1e6QBwJvEu0AHgTEWgA4AnCHQA8ASBDgCeINABwBMEOgB4gkAHAE+EHehmFmdm683shUgUBADomUj00O+SVBiB4wAAwhBWoJvZGEmflbQoMuUAAHoq3B76A5J+LCkYgVoAAGHocaCb2ZWSKp1zp3xEkJndZmb5ZpZfVVXV09MBAE4jnB76XElXm9kuSUskXWpmHZ7U7Jxb6JzLc87lZWRkhHE6AMCp9DjQnXM/cc6Ncc5NkHS9pFedc1+NWGUAgG5hHToAeCIiD7hwzr0u6fVIHAsA0DP00AHAEwQ6AHiCQAcATxDoAOAJAh0APEGgA4AnCHQA8ASBDgCeINABwBMEOgB4gkAHAE8Q6ADgCQIdADxBoAOAJwh0APAEgQ4AniDQAcATBDoAeIJABwBPEOgA4AkCHQA8QaADgCcIdADwBIEOAJ4g0AHAEwQ6AHiCQAcATxDoAOAJAh0APEGgA4AnCHQA8ASBDgCeINABwBMEOgB4gkAHAE8Q6ADgCQIdADxBoAOAJwh0APAEgQ4AniDQAcATBDoAeIJABwBPEOgA4AkCHQA8QaADgCcIdADwBIEOAJ4g0AHAEz0OdDMba2avmVmhmW02s7siWRgAoHviw9i3WdIPnXPrzGygpAIze8U5tyVCtQEAuqHHPXTnXLlzbl3b90clFUrKilRhAIDuicgYuplNkDRd0upIHA8A0H1hB7qZpUn6u6S7nXNHQrx/m5nlm1l+VVVVuKcDAHQirEA3swS1hvmTzrlnQm3jnFvonMtzzuVlZGSEczoAwCmEs8rFJP1eUqFz7v7IlQQA6IlweuhzJX1N0qVmtqHt12ciVBcAoJt6vGzROfe2JItgLQCAMHClKAB4gkAHAE8Q6ADgCQIdADxBoAOAJwh0APAEgQ4AniDQAcATBDoAeIJABwBPEOgA4AkCHQA8QaADgCcIdADwBIEOAJ4g0AHAEwQ6AHiCQAcATxDoAOAJAh0APEGgA4AnCHQA8ASBDgCeINABwBMEOgB4gkAHAE8Q6ADgCQIdADxBoAOAJwh0APAEgQ4AniDQAcATBDoAeIJABwBPEOgA4AkCHQA8QaADgCcIdADwBIEOAJ4g0AHAE/GxLgAAfHGoolb799bo6IF6tbQEFRcX0MBhyRo+Jk1DMlOjfn4CHQDC0FDbpM1vlWnrqnId3Ffb6XZDR6Zq0uxRmvKJ0UpKTYhKLQQ6APSACzptWLFHBS/tUkNt82m3P7ivVqv+sUPrlu/WBZ+eoI9dNlYWsIjWRKADQDc11DZp+aLN2rOlugf7Nmvl34u1p7Ba8781JaK9de8mRVsaGlR/8GCsywDgqYbaJi19cIP2rt8Z1nH2bKnW0gc3qKG2KUKV9aNAbwm2aPOBzVq8dbEe3fioFm9drM0HNqsl2CJJCra0aOdzz2nFN7+p+OTkGFcLwEcu6LR80WZV7j6qpMo1St3+V1lDzzuQlbuPavmizXJBF5H6+vyQi3NOzxY/q8fee0ylNaUd3s8aMFrfavqkUv72rg4XFenjv/iF4lNSYlApAN9tWLHn+DBL/ehLNHjtL5RYla+G0ZeofszlcgmpSkyO0+icIUofnabqshqVFR1SY31Lp8fcs6VaG1bs0fTLx4VdX58O9NqmWv3gjR/ondJ3Ot2m/Eip3nrjz5pVJKWdNUFnX3tt7xUI4IzRUNukgpd2fdQQl6S68Z/RgOK/KbEyX3GTPqk5X5ui7Bkj2k12uqBTcUGlVv6jWDXVDSGPXfDSLk2eOyrs8fQ+O+TinDttmEtSVpk0dbO09gJp9aUpsri4XqoQwJlk81tlHVazNGbOVsOImUrKzNLEpFWaOH14h5UrFjDlzMzUDT+bpXM+nhny2A21zdr8dlnYNYYV6Ga2wMy2mVmxmd0TdjUneLb42dOG+dg9Tp9/1um5q0yvzjMtTd+q53Y8F8kyAECStHVVecfGQJwCs27WlUseV0NVpd79t39TsCX08EpicrwuuTFXaUOTQh9/ZYjjd1OPA93M4iT9RtKnJU2WdIOZTQ67IrVOgD723mMd2l3Q6ejGo6pcWqlhrx07Hua7JpiCcSaZ6dGNjx6fKAWASDhUUdvpRUNzvjBJKUPSdMlvf6u6ffu06qc/1R8eflJ33PRD/eG3i9XS/FEeJSbHa/bnJ4Y8zsF9tTpU0fmFSV0RTg/945KKnXM7nXONkpZIuiasatpsPbi1wwSoCzqV/LpEu3+1W+nLanT9qgQtbK7UByfNI5TWlGrbwW2RKAMAJEn799aEbE9MjlP2BSMkSfEpKbrooV/r7ReWa81//1iP/fl+ffM7N2rujE+1C/WcCzKVkBx6aPhAaejzdFU4gZ4lac8Jr/e2tYXtvar3OrTVbKrR0fVHNSQ+XneOGaOHS0u1duN+1Wzq+BuwsWpjJMoAAEnS0QP1IdtH5wxpN2b+1z8/r58Vvqf0hAR9LiNDkrR60+v608Knjm9jAdPonCEhj3dkf+jzdFU4gR7qmtUOiynN7DYzyzez/Kqqqi4d+HDD4Q5tdbvrJEmHmpv1bzt3avOxY+3aT7c/APRUS0swZHv66LR2r9e8m69G53RfSYmWHzhwvH3tuwXttht20n6nO09XhRPoeyWNPeH1GEkdpmmdcwudc3nOubyMtv+xTmdw0uAObSnjP1pbXt3cHLL9VPsDQE/FxYWOyuqy9iMEH78wT5LU6JyOBT8K55kXXtBuuwNloYdWOjtPV4Wz91pJOWZ2lpklSrpe0tKwqmlzfsb5HdrSpqZp4PSB7doGTh+otKkd/6ebljEtEmUAgCRp4LDQV5+XFR1qd5XnTbd9WbOmzmu3zayp83TTbV8+/toFncqKDoU83qDh4V3l3uMLi5xzzWb2XUnLJcVJetw5tzmsatpMGjpJWWlZ7SZGLWAa971xqtlUo7rddUoZn6K0qWkd1nxmpWUpd2huJMoAAEnS8DGhh0ga61tUXFCpnJmt68vj4uP0zrp/6k8Ln9Ladws088ILdNNtX1Zc/EeToEUFFWrq5MrRYVmhz9NVYV0p6px7UdKLYVUQQlwgTv9y/r/oZyt/1q7dAqaB0wZq4LSBnewp3T7tdsUFuLgIQOQMyUzV0JGpIZcurvxHsSacP1wJSa25Excfp5u/fYNu/vYNHbZtrG/Wqmd2hDzH0JGpYT8Eo89eKXpt9rWamzW3W/vMzZqrayZGZOUkALQzafaokO011Q16/cmtaqw/9T3RG+ub9cZft6nmYOjL/yfNCX387uizgW5muv+S+7sc6nOz5ur+S+6XWWRvGA8AktqeNBR6UGP7mgot/sVqFa2t6HDnRBd0Klrb+v72NRUh909KjdeUi0aHXaM5F5nbNnZFXl6ey8/P79Y+zjk9t+M5Pbrx0dB3W0zL0u3Tbtc1E68hzAFE1fpXSrTy78Wn3Cah7W6Lw0an6UDb3RY7GzP/0JwvZJ/ybotmVuCcyztdfX0+0D/UEmzRtoPbtLFqow43HNbgpMGaljFNuUNzGTMH0Ctc0On5hzf26ElFnRk3OV1XfnfaKR9H19VA79O3zz1RXCBOk4dN1uRhEbldDAB0mwVM8781RUsf3KDK3UfDPt6I8QN1xbemROzZon12DB0A+qKk1ARdfdfHNHZyeljHGTs5XVff9bGIPlO03/TQAaCvSEpN0FXfnaYNK/ao4KVdHe6Tfup943XBpyfoY5eNjVjP/EMEOgD0gAVM0y8fp8lzR2nz22XaurK801vsSq3rzCfNGaUpF42OaK/8RAQ6AIQhKTVBM64YrxlXjNehilodKK3Rkf31amkJKi4uoEHDkzUsKy3si4a6gkAHgAgZkhn+1Z7hYFIUADxBoAOAJwh0APBEr14pamZVknZH4FDDJe2PwHH6izPp855Jn1Xi8/oskp91vHPutE8I6tVAjxQzy+/KZbC+OJM+75n0WSU+r89i8VkZcgEATxDoAOCJ/hroC2NdQC87kz7vmfRZJT6vz3r9s/bLMXQAQEf9tYcOADhJvwt0M1tgZtvMrNjM7ol1PdFiZmPN7DUzKzSzzWZ2V6xr6g1mFmdm683shVjXEm1mNsTMnjazrW1/zrNjXVO0mNn32/4ev29mi80sOdY1RZKZPW5mlWb2/glt6Wb2ipkVtX0dGu06+lWgm1mcpN9I+rSkyZJuMDNfn3jRLOmHzrlzJV0o6Tsef9YT3SWpMNZF9JIHJS1zzk2SNE2efm4zy5J0p6Q859x5kuIkXR/bqiLuj5IWnNR2j6QVzrkcSSvaXkdVvwp0SR+XVOyc2+mca5S0RNI1Ma4pKpxz5c65dW3fH1XrP/as2FYVXWY2RtJnJS2KdS3RZmaDJF0s6feS5JxrdM4dim1VURUvKcXM4iWlSiqLcT0R5Zx7U9LJz6W7RtITbd8/IenaaNfR3wJA7IXNAAAB7UlEQVQ9S9KeE17vlechJ0lmNkHSdEmrY1tJ1D0g6ceSgrEupBecLalK0h/ahpgWmdmAWBcVDc65Ukn3SSqRVC7psHPu5dhW1SsynXPlUmsHTdKIaJ+wvwV6qMd7eL1Mx8zSJP1d0t3OuSOxridazOxKSZXOuYJY19JL4iXNkPSIc266pGPqhR/JY6Ft7PgaSWdJGi1pgJl9NbZV+am/BfpeSWNPeD1Gnv3odiIzS1BrmD/pnHsm1vVE2VxJV5vZLrUOpV1qZn+JbUlRtVfSXufchz91Pa3WgPfRpyR94Jyrcs41SXpG0pwY19QbKsxslCS1fa2M9gn7W6CvlZRjZmeZWaJaJ1aWxrimqDAzU+v4aqFz7v5Y1xNtzrmfOOfGOOcmqPXP9VXnnLe9OOfcPkl7zCy3rekySVtiWFI0lUi60MxS2/5eXyZPJ4BPslTS19u+/7qk56J9wn71xCLnXLOZfVfScrXOlD/unNsc47KiZa6kr0naZGYb2tp+6px7MYY1IbK+J+nJts7JTkk3x7ieqHDOrTazpyWtU+vqrfXy7IpRM1ssaZ6k4Wa2V9LPJd0r6Skzu0Wt/6l9Kep1cKUoAPihvw25AAA6QaADgCcIdADwBIEOAJ4g0AHAEwQ6AHiCQAcATxDoAOCJ/w8DnTgF3d1XpwAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(6, 6))\n",
"fig = plt.figure(figsize=(6, 6))\n",
"g = Ground()\n",
"g.add_point(MaterialPoint(x0=10, y0=10, mass=4, v_x0=-2, v_y0=-2))\n",
"g.add_point(MaterialPoint(x0=5, y0=10, mass=3, v_x0=-2, v_y0=-2))\n",
"g.add_point(MaterialPoint(x0=0, y0=0, mass=10, v_x0=2, v_y0=2))\n",
"g.add_point(MaterialPoint(x0=0, y0=10, mass=12, v_x0=2, v_y0=-2))\n",
"g.add_point(MaterialPoint(x0=10, y0=0, mass=20, v_x0=-2, v_y0=2))\n",
"g.add_point(MaterialPoint(x0=4, y0=10, mass=15, v_x0=-2, v_y0=-2))\n",
"\n",
"g.add_point(MaterialPoint(x0=0, y0=5, mass=6, v_x0=2, v_y0=-4))\n",
"g.add_point(MaterialPoint(x0=10, y0=5, mass=8, v_x0=-2, v_y0=2))\n",
"g.calculate_speed_points(end_time=100)\n",
"points = g.points\n",
"\n",
"size = len(g.points[0].x_args)\n",
"anim = animation.FuncAnimation(fig, g.update_HTML_animation,interval=40,fargs=(fig,),frames=size, blit=False)\n",
"HTML(anim.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The total energy of closed mechanics system in which does not act any external forces remains the same\n",
"$$\\frac{dH}{dt}=\\sum{\\frac{dE_i}{dt}} = 0 \\Leftrightarrow H=Const $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"REFERENCES: \n",
"[1] https://en.wikipedia.org/wiki/Work_(physics) \n",
"[2] Numerical Methods for Solving Systems of Nonlinear Euqtions by Courtney Remani \n",
"[3] http://www.astro.utu.fi/~cflynn/galdyn/lecture6.html?fbclid=IwAR31E-ezjjqEmMxxui7CkpEjrc32ACuMErAHQgK1sSsaifNRv2ss3FcPGaY \n",
"[4] https://www.quora.com/What-is-the-relationship-between-mass-and-velocity \n",
"[5] Stability of the Leapfrog/Midpoint Method\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}