RK_Simulation.ipynb

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      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uJqDYeY7Ljwb"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import scipy.special as sp"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def CarToSph(xyz):\n",
        "    if len(xyz.shape) == 2:\n",
        "        x, y, z = xyz[:,0], xyz[:,1], xyz[:,2]\n",
        "    elif len(xyz.shape) == 1:\n",
        "        x, y, z = xyz[0], xyz[1], xyz[2]\n",
        "    r = np.sqrt(x ** 2 + y ** 2 + z ** 2)\n",
        "    theta = np.arccos(z/r)\n",
        "    phi = np.arctan2(y, x)\n",
        "    return r, theta, phi\n",
        "\n",
        "\n",
        "def SphToCar(r, theta, phi):\n",
        "    x = r * np.cos(phi) * np.sin(theta)\n",
        "    y = r * np.sin(phi) * np.sin(theta)\n",
        "    z = r * np.cos(theta)\n",
        "    return x, y, z\n"
      ],
      "metadata": {
        "id": "tSC-7j5kMa1U"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def XYZToL(idx, level):\n",
        "    n = 2 ** level\n",
        "    return idx[2] * n * n +idx[1] * n + idx[0]\n",
        "\n",
        "\n",
        "def LToXYZ(l, level):\n",
        "    n = 2 ** level\n",
        "    z = l // (n * n)\n",
        "    y = (l-z * n * n)//n\n",
        "    x = (l-z * n * n) % n\n",
        "    return np.array([x, y, z])\n"
      ],
      "metadata": {
        "id": "gzE7oJp7MgTq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Code for the beginning of the model."
      ],
      "metadata": {
        "id": "THnmZTGCMlGo"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy\n",
        "import scipy.integrate\n",
        "import astropy\n",
        "import astropy.constants as c\n",
        "\n",
        "\n",
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "from matplotlib.animation import FFMpegWriter"
      ],
      "metadata": {
        "id": "A6SQDAU2VjKm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class Vector:\n",
        "    def __init__(self, x, y):\n",
        "        self.x = x\n",
        "        self.y = y\n",
        "\n",
        "    def add(self, other):\n",
        "        return Vector(self.x + other.x, self.y + other.y)\n",
        "\n",
        "    def sub(self, other):\n",
        "        return Vector(self.x - other.x, self.y - other.y)\n",
        "\n",
        "    def div(self, c):\n",
        "        return Vector(self.x / c, self.y / c)\n",
        "\n",
        "    def mult(self, c):\n",
        "        return Vector(self.x / c, self.y / c)\n",
        "\n",
        "    def mag(self):\n",
        "        return math.sqrt(self.x * self.x + self.y * self.y)\n",
        "\n",
        "    def norm(self):\n",
        "        if self.x == 0 and self.y == 0:\n",
        "            return Vector(0,0)\n",
        "        else:\n",
        "            return self.div(self.mag())\n",
        "\n",
        "    def dot(self, other):\n",
        "        return self.x * other.x + self.y * other.y\n",
        "\n",
        "    def anglebet(self, other):\n",
        "        return math.acos(dot(self, other) / (mag(x) + mag(y)))\n",
        "\n",
        "    def display(self):\n",
        "        print(\"[\", self.x, \" \" , self.y , \"]\");\n",
        "\n",
        "    def toarray(self):\n",
        "        return np.array([self.x, self.y])"
      ],
      "metadata": {
        "id": "PXCUt4lXnHl8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#This is just defining our class, and methods of the objects\n",
        "class Asteroid:\n",
        "    def __init__(self, pos, velo, mass, r):\n",
        "        self.pos = pos\n",
        "        self.velo = velo\n",
        "        self.mass = mass\n",
        "        self.r = r\n",
        "\n",
        "    def distance(self, other):\n",
        "        temp = (self.pos.x - other.pos.x) **2 + (self.pos.y - other.pos.y) **2\n",
        "        return abs(math.sqrt(temp))  #This is just finding the distance btw the objects\n",
        "\n",
        "    def calc_grav_force(self,mass,r):\n",
        "        return (c.G * (mass*(2e21)) / (r) ** 2) #This is the gravitational force btw the two objects. 2e21 is jsut the mass of the plaent\n",
        "\n",
        "    def KN(self,mass,velo):\n",
        "        return 0.5 * mass * velo ** 2\n",
        "\n",
        "dimorphos = Asteroid(Vector(0,-4), Vector(20,0), 4.52e9, 278.87)\n",
        "didymos = Asteroid(Vector(0,0), Vector(0,0), 5.24e11, 1279.5)"
      ],
      "metadata": {
        "id": "IAJoGwQaVkPd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class spacecraft:\n",
        "    def __init__(self, Pos_1, Velo_1, Mass_1, R):\n",
        "        self.Velo_1 = Velo_1  #Need to figure out what type of velocity\n",
        "        self.Mass_1 = Mass_1\n",
        "        self.Pos_1 = Pos_1\n",
        "        self.R = R\n",
        "\n",
        "    def KN (self,Mass_1,Velo_1):\n",
        "        return ((1/2) * (Mass_1) * Velo_1.mag() **2)\n",
        "\n",
        "spacecraft_1 = spacecraft(Vector(10,-4), Vector(0,0),610,1)\n"
      ],
      "metadata": {
        "id": "GVkPITg9djJw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Animating a binary system"
      ],
      "metadata": {
        "id": "TneSbRQEVkvg"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "G = 1 #gravitational constant\n",
        "\n",
        "# Define masses (in terms of solar mass)\n",
        "m1 = 4.52e0   # (Smaller)\n",
        "m2 = 5.24e2  # (Bigger)\n",
        "\n",
        "# Define initial position vectors\n",
        "r1 = np.array([2,0])\n",
        "r2 = np.array([0,0])\n",
        "\n",
        "# Define initial velocities\n",
        "v1 = np.array([0,1])\n",
        "v2 = np.array([0,0])\n",
        "\n",
        "#Initialize new instances of the Star Class\n",
        "Didy = (m1,r1,v1)\n",
        "Dimor = (m2,r2,v2)"
      ],
      "metadata": {
        "id": "gkjov7YMVrHz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def TwoBodyEquations(w, t, m1, m2): # w is an array containing positions and velocities\n",
        "\n",
        "    r1 = w[:2]\n",
        "    r2 = w[2:4]\n",
        "    v1 = w[4:6]\n",
        "    v2 = w[6:8]\n",
        "\n",
        "\n",
        "    r12 = np.linalg.norm(r2-r1)\n",
        "\n",
        "    dv1bydt = m2*(r2-r1)/r12 **3  # derivative of velocity\n",
        "    dv2bydt = m1*(r1-r2)/r12 **3\n",
        "\n",
        "    dr1bydt = v1 # derivative of position\n",
        "    dr2bydt = v2\n",
        "\n",
        "    r_derivs = np.concatenate((dr1bydt,dr2bydt)) # joining arrays together\n",
        "    v_derivs = np.concatenate((dv1bydt,dv2bydt))\n",
        "    derivs = np.concatenate((r_derivs,v_derivs))\n",
        "\n",
        "    return derivs"
      ],
      "metadata": {
        "id": "P_n82ucGVrXF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Package initial parameters into one array (just easier to work with this way)\n",
        "init_params = np.array([r1, r2, v1, v2], dtype=np.float64)\n",
        "init_params = init_params.flatten()\n",
        "time_span = np.linspace(0, 5, 500)  # run for t=5 (500 points)\n",
        "\n",
        "# Run the ODE solver\n",
        "two_body_sol = scipy.integrate.odeint(TwoBodyEquations, init_params, time_span, args=(m1,m2))"
      ],
      "metadata": {
        "id": "adVGHmCTEYbL"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "r1_sol = two_body_sol[:,:2]\n",
        "r2_sol = two_body_sol[:,2:4]"
      ],
      "metadata": {
        "id": "_n1VvW8dEc6z"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Initilize writer\n",
        "metadata = dict(title='My first animation', artist='Matplotlib')\n",
        "writer = FFMpegWriter(fps=50, metadata=metadata, bitrate=200000) # change fps for different frame rates\n",
        "fig = plt.figure(dpi=200)"
      ],
      "metadata": {
        "id": "KzDra7MUEhOQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "afff61b7-e5e7-43d6-f601-a6645f95932b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x800 with 0 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# SAVE AS MP4 (will be saved in whatever directory you are working in) ##infinite loop fix\n",
        "fig, ax = plt.subplots()\n",
        "\n",
        "with writer.saving(fig, \"orbit.mp4\", dpi=200):\n",
        "    for i in range(len(time_span)):\n",
        "\n",
        "        ax.clear()\n",
        "\n",
        "        ax.plot(r1_sol[:i,0],r1_sol[:i,1], color=\"blue\", alpha=0.5)\n",
        "        ax.scatter(r1_sol[i,0],r1_sol[i,1], color=\"blue\", marker=\"o\",s=20, zorder=5) # planet\n",
        "\n",
        "        ax.scatter(0, 0, color=\"orange\", marker=\"*\",s=50, zorder=5) # star\n",
        "\n",
        "        ax.set_xlim(-10, 10)\n",
        "        ax.set_ylim(-10, 10)\n",
        "\n",
        "        plt.draw()\n",
        "        plt.pause(0.01)\n",
        "        writer.grab_frame()"
      ],
      "metadata": {
        "id": "hxP4toGZElvv",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "3f6e27e7-ef27-45b5-9eb1-333de42b3155"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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    {
      "cell_type": "markdown",
      "source": [
        "## RK4 Kernel\n",
        "A forth-order high accuracy ODE solver."
      ],
      "metadata": {
        "id": "E8OXT7wIAVRE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Structure of ``` pair ```:\n",
        "\n",
        "```\n",
        "array([[0, 1],\n",
        "    [0, 2],\n",
        "    [3, 4]])\n",
        "```\n",
        "First column for the small mass \\\\\n",
        "Second column for the big\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "uhwC8pCgRyZ_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def NBodyDerivs_slow(w, t, m, pair):\n",
        "  n = w.shape[1]\n",
        "  r = w[:2,:]\n",
        "  v = w[2:,:]\n",
        "  r_derivs = v\n",
        "  v_derivs = np.zeros(shape=r_derivs.shape)\n",
        "  for i in range(pair.shape[0]):\n",
        "    rr = np.linalg.norm(r[:,pair[i,0]] - r[:,pair[i,1]], axis=0)\n",
        "    v_derivs[:,pair[i,0]] += (m[pair[i,1]]*(r[:,pair[i,1]]-r[:,pair[i,0]])/rr**3)\n",
        "  return np.concatenate((r_derivs,v_derivs))"
      ],
      "metadata": {
        "id": "AOtOCoFrmGJi"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def NBodyDerivs(w, t, m, pair): # Faster when the number of particle >= 4\n",
        "  n = w.shape[1]\n",
        "  r = w[:2,:]\n",
        "  v = w[2:,:]\n",
        "  rr = np.linalg.norm(r[:,pair[:,0]] - r[:,pair[:,1]], axis=0)\n",
        "  SUM = np.zeros(shape=(pair.shape[0], n))\n",
        "  SUM[np.arange(pair.shape[0]), pair[:,0]] = 1\n",
        "  v_derivs = (m[pair[:,1]]*(r[:,pair[:,1]]- r[:,pair[:,0]])/rr**3) @ SUM\n",
        "  return np.concatenate((v,v_derivs))"
      ],
      "metadata": {
        "id": "tBGOi8y0Jx4e"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def f(t,y):\n",
        "  return NBodyDerivs(y, t, m, pair)"
      ],
      "metadata": {
        "id": "ZbKOqI1Imysr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "r1 = [0,0.5]\n",
        "r2 = [0,0]\n",
        "v1 = [-1,0]\n",
        "v2 = [1,0]\n",
        "m = np.array([1,1])\n",
        "pair = np.array([[0,1],[1,0]])\n",
        "init_condition = np.vstack((np.stack((r1,r2)).T, np.stack((v1,v2)).T))"
      ],
      "metadata": {
        "id": "ejCN5kTKkgZF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def solve_orbit(init, start_t, total_t, dt):\n",
        "  t, y = start_t, init\n",
        "  h = dt\n",
        "\n",
        "  ans = np.zeros(shape=(4,2,int(total_t/dt)//100+1), dtype=np.float64)\n",
        "\n",
        "  step = 0\n",
        "\n",
        "  while t<start_t+total_t:\n",
        "    k1 = f(t, y)\n",
        "    k2 = f(t+0.5*h, y+0.5*h*k1)\n",
        "    k3 = f(t+0.5*h, y+0.5*h*k2)\n",
        "    k4 = f(t+h, y+h*k3)\n",
        "    y += h/6.*(k1+2.*k2+2.*k3+k4)\n",
        "    t += h\n",
        "    if step % 100 == 0:\n",
        "      ans[:,:,step//100] = y.copy()\n",
        "    step += 1\n",
        "  return ans[:,:,:-1]\n",
        "\n",
        "def solve_orbit_with_inject(init, start_t, total_t, dt, rotate, lost_rate):\n",
        "  t, y = start_t, init\n",
        "  h = dt\n",
        "\n",
        "  ans = np.zeros(shape=(4,2,int(total_t/dt)//100+1), dtype=np.float64)\n",
        "\n",
        "  step = 0\n",
        "\n",
        "  while t<start_t+total_t:\n",
        "    k1 = f(t, y)\n",
        "    k2 = f(t+0.5*h, y+0.5*h*k1)\n",
        "    k3 = f(t+0.5*h, y+0.5*h*k2)\n",
        "    k4 = f(t+h, y+h*k3)\n",
        "    y += h/6.*(k1+2.*k2+2.*k3+k4)\n",
        "    y[2,0] += np.cos(2*np.pi*t/rotate)*lost_rate\n",
        "    y[3,0] += np.sin(2*np.pi*t/rotate)*lost_rate\n",
        "    t += h\n",
        "    if step % 100 == 0:\n",
        "      ans[:,:,step//100] = y.copy()\n",
        "    step += 1\n",
        "  return ans[:,:,:-1]\n"
      ],
      "metadata": {
        "id": "5KzT8MbpCyEb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "r1 = [0,30.]\n",
        "r2 = [0,0]\n",
        "v1 = [-2,0]\n",
        "v2 = [0,0]\n",
        "m = np.array([1,100], dtype=np.float64)\n",
        "pair = np.array([[0,1]])\n",
        "init_condition = np.vstack((np.stack((r1,r2)).T,np.stack((v1,v2)).T))\n",
        "ans_original = solve_orbit(init_condition.copy(), 0, 130., 0.01)"
      ],
      "metadata": {
        "id": "LAkYmpiIpYCx"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Parameters { run: \"auto\", form-width: \"400px\" }\n",
        "plt.figure(figsize=(12,10))\n",
        "InjectionRate1 = 5e-5 #@param {type:\"slider\", min:0, max:0.05, step:100}\n",
        "InjectionRate2 = 5e-4\n",
        "InjectionRate3 = 5e-3\n",
        "SpinPeriod = 3.2 #@param {type:\"slider\", min:1, max:200, step:100}\n",
        "plt.scatter(ans_original[0,1,:],ans_original[1,1,:], label=\"Central Astriod\")\n",
        "plt.scatter(ans_original[0,0,:],ans_original[1,0,:], label=\"Before Impact\", color = '#674ea7')\n",
        "inti = ans_original[:,:,-1].copy()\n",
        "inti[3,0] -= 0.02 # Impact Factor\n",
        "ans = solve_orbit_with_inject(inti, 130, 140., 0.01, SpinPeriod, InjectionRate1)\n",
        "plt.scatter(ans[0,0,:],ans[1,0,:], label=\"After Impact - Low Injection Rate\", color = '#45818e')\n",
        "ans = solve_orbit_with_inject(inti, 130, 140., 0.01, SpinPeriod, InjectionRate2)\n",
        "plt.scatter(ans[0,0,:],ans[1,0,:], label=\"After Impact - Medium Injection Rate\", color = '#76a5af')\n",
        "ans = solve_orbit_with_inject(inti, 130, 140., 0.01, SpinPeriod, InjectionRate3)\n",
        "plt.scatter(ans[0,0,:],ans[1,0,:], label=\"After Impact - High Injection Rate\", color = '#a2c4c9')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "3Vb0oktVn8Za",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 592
        },
        "outputId": "744f9ef7-c93d-4130-cfb7-65cb543ac721"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "9uR35yvSJBBZ"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}