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{
"cells": [
{
"cell_type": "code",
"execution_count": 213,
"metadata": {},
"outputs": [],
"source": [
"def eulerstep(state, rhs, dt):\n",
" '''Update a state to the next time increment using Euler's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" \n",
" next_state = state + rhs(state) * dt\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 214,
"metadata": {},
"outputs": [],
"source": [
"def rk2_step(state, rhs, dt):\n",
" '''Update a state to the next time increment using modified Euler's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" \n",
" mid_state = state + rhs(state) * dt*0.5 \n",
" next_state = state + rhs(mid_state)*dt\n",
" \n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 215,
"metadata": {},
"outputs": [],
"source": [
"def heun_step(state,rhs,dt,etol=0.000001,maxiters = 100):\n",
" '''Update a state to the next time increment using the implicit Heun's method.\n",
" \n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" etol : tolerance in error for each time step corrector\n",
" maxiters: maximum number of iterations each time step can take\n",
" \n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" e=1\n",
" eps=np.finfo('float64').eps\n",
" next_state = state + rhs(state)*dt\n",
" ################### New iterative correction #########################\n",
" for n in range(0,maxiters):\n",
" next_state_old = next_state\n",
" next_state = state + (rhs(state)+rhs(next_state))/2*dt\n",
" e=np.sum(np.abs(next_state-next_state_old)/np.abs(next_state+eps))\n",
" if e<etol:\n",
" break\n",
" ############### end of iterative correction #########################\n",
" return next_state"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Initial Value Problems - Project\n",
"\n",
"![Initial condition of firework with FBD and sum of momentum](../images/firework.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are going to end this module with a __bang__ by looking at the flight path of a firework. Shown above is the initial condition of a firework, the _Freedom Flyer_ in (a), its final height where it detonates in (b), the applied forces in the __Free Body Diagram (FBD)__ in (c), and the __momentum__ of the firework $m\\mathbf{v}$ and the propellent $dm \\mathbf{u}$ in (d). \n",
"\n",
"The resulting equation of motion is that the acceleration is proportional to the speed of the propellent and the mass rate change $\\frac{dm}{dt}$ as such\n",
"\n",
"$$\\begin{equation}\n",
"m\\frac{dv}{dt} = u\\frac{dm}{dt} -mg - cv^2.~~~~~~~~(1)\n",
"\\end{equation}$$\n",
"\n",
"If we assume that the acceleration and the propellent momentum are much greater than the forces of gravity and drag, then the equation is simplified to the conservation of momentum. A further simplification is that the speed of the propellant is constant, $u=constant$, then the equation can be integrated to obtain an analytical rocket equation solution of [Tsiolkovsky](https://www.math24.net/rocket-motion/) [1,2], \n",
"\n",
"$$\\begin{equation}\n",
"m\\frac{dv}{dt} = u\\frac{dm}{dt}~~~~~(2.a)\n",
"\\end{equation}$$\n",
"\n",
"$$\\begin{equation}\n",
"\\frac{m_{f}}{m_{0}}=e^{-\\Delta v / u},~~~~~(2.b) \n",
"\\end{equation}$$\n",
"\n",
"where $m_f$ and $m_0$ are the mass at beginning and end of flight, $u$ is the speed of the propellent, and $\\Delta v=v_{final}-v_{initial}$ is the change in speed of the rocket from beginning to end of flight. Equation 2.b only relates the final velocity to the change in mass and propellent speed. When you integrate Eqn 2.a, you will have to compare the velocity as a function of mass loss. \n",
"\n",
"Your first objective is to integrate a numerical model that converges to equation (2.b), the Tsiolkovsky equation. Next, you will add drag and gravity and compare the results _between equations (1) and (2)_. Finally, you will vary the mass change rate to achieve the desired detonation height. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. Create a `simplerocket` function that returns the velocity, $v$, the acceleration, $a$, and the mass rate change $\\frac{dm}{dt}$, as a function of the $state = [position,~velocity,~mass] = [y,~v,~m]$ using eqn (2.a). Where the mass rate change $\\frac{dm}{dt}$ and the propellent speed $u$ are constants. The average velocity of gun powder propellent used in firework rockets is $u=250$ m/s [3,4]. \n",
"\n",
"$\\frac{d~state}{dt} = f(state)$\n",
"\n",
"$\\left[\\begin{array}{c} v\\\\a\\\\ \\frac{dm}{dt} \\end{array}\\right] = \\left[\\begin{array}{c} v\\\\ \\frac{u}{m}\\frac{dm}{dt} \\\\ \\frac{dm}{dt} \\end{array}\\right]$\n",
"\n",
"Use [two integration methods](../notebooks/03_Get_Oscillations.ipynb) to integrate the `simplerocket` function, one explicit method and one implicit method. Demonstrate that the solutions converge to equation (2.b) the Tsiolkovsky equation. Use an initial state of y=0 m, v=0 m/s, and m=0.25 kg. \n",
"\n",
"Integrate the function until mass, $m_{f}=0.05~kg$, using a mass rate change of $\\frac{dm}{dt}=0.05$ kg/s. \n",
"\n",
"_Hint: your integrated solution will have a current mass that you can use to create $\\frac{m_{f}}{m_{0}}$ by dividing state[2]/(initial mass), then your plot of velocity(t) vs mass(t)/mass(0) should match Tsiolkovsky's_"
]
},
{
"cell_type": "code",
"execution_count": 216,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"plt.rcParams.update({'font.size': 22})\n",
"plt.rcParams['lines.linewidth'] = 3"
]
},
{
"cell_type": "code",
"execution_count": 217,
"metadata": {},
"outputs": [],
"source": [
"def simplerocket(state,dmdt=0.05, u=250):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, without drag or gravity, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" \n",
" Returns\n",
" -------\n",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" \n",
" dstate = np.array([state[1], (u/state[2])*dmdt, -dmdt])\n",
" \n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 218,
"metadata": {},
"outputs": [],
"source": [
"#Constants and Initial Values\n",
"y0 = 0\n",
"v0 = 0\n",
"m0 = 0.25\n",
"u = 250\n",
"mf = 0.05"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Runge Kutta Two Step**"
]
},
{
"cell_type": "code",
"execution_count": 286,
"metadata": {},
"outputs": [],
"source": [
"#initialize Time Array\n",
"N = 40\n",
"dmdt = 0.05\n",
"u = 250\n",
"tf = (m0-mf)/dmdt\n",
"t = np.linspace(0,tf,N) \n",
"dt = t[1]-t[0]\n",
"\n",
"#initialize solution array\n",
"sol_rk2 = np.zeros([N,3])\n",
"\n",
"sol_rk2[0,0] = y0\n",
"sol_rk2[0,1] = v0\n",
"sol_rk2[0,2] = m0\n",
"\n",
"#Integration using Explicit Method: Modified Euler Runge Kutta two step\n",
"for i in range(N-1):\n",
" sol_rk2[i+1] = rk2_step(sol_rk2[i], simplerocket, dt)\n",
"\n",
"mt_rk2 = sol_rk2[:,2]/m0\n",
"v_rk2 = sol_rk2[:,1]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Analytical**"
]
},
{
"cell_type": "code",
"execution_count": 287,
"metadata": {},
"outputs": [],
"source": [
"# Anlytical Solution: Tsiokovsky Solution\n",
"mt = np.linspace(m0,mf,N+1)\n",
"dm = mt/m0\n",
"vf = -250*np.log(dm)"
]
},
{
"cell_type": "code",
"execution_count": 288,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(dm, vf, label=\"Tsiokovsky Solution\", linestyle ='dashed')\n",
"plt.plot(mt_rk2, v_rk2, label=\"Runge Kutta\")\n",
"\n",
"plt.title(\"Simplerocket Mass Ratio vs. Velocity\")\n",
"plt.xlabel(\"mf/m0 [kg]\")\n",
"plt.ylabel(\"Velocity [m/s]\")\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Heun's Method**"
]
},
{
"cell_type": "code",
"execution_count": 289,
"metadata": {},
"outputs": [],
"source": [
"#initialize solution array\n",
"sol_heun = np.zeros([N,3])\n",
"\n",
"sol_heun[0,0] = y0\n",
"sol_heun[0,1] = v0\n",
"sol_heun[0,2] = m0\n",
"\n",
"#Integration using Implicit Method: Heun Step\n",
"for i in range(N-1):\n",
" sol_heun[i+1] = heun_step(sol_heun[i], simplerocket, dt)\n",
"\n",
"mt_heun = sol_heun[:,2]/m0\n",
"v_heun = sol_heun[:,1]"
]
},
{
"cell_type": "code",
"execution_count": 290,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(dm, vf, label=\"Tsiokovsky Solution\")\n",
"plt.plot(mt_heun, v_heun, label=\"Heun\", linestyle = 'dashed')\n",
"\n",
"plt.title(\"Simplerocket Mass Ratio vs. Velocity\")\n",
"plt.xlabel(\"mf/m0 [kg]\")\n",
"plt.ylabel(\"Velocity [m/s]\")\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. You should have a converged solution for integrating `simplerocket`. Now, create a more relastic function, `rocket` that incorporates gravity and drag and returns the velocity, $v$, the acceleration, $a$, and the mass rate change $\\frac{dm}{dt}$, as a function of the $state = [position,~velocity,~mass] = [y,~v,~m]$ using eqn (1). Where the mass rate change $\\frac{dm}{dt}$ and the propellent speed $u$ are constants. The average velocity of gun powder propellent used in firework rockets is $u=250$ m/s [3,4]. \n",
"\n",
"$\\frac{d~state}{dt} = f(state)$\n",
"\n",
"$\\left[\\begin{array}{c} v\\\\a\\\\ \\frac{dm}{dt} \\end{array}\\right] = \n",
"\\left[\\begin{array}{c} v\\\\ \\frac{u}{m}\\frac{dm}{dt}-g-\\frac{c}{m}v^2 \\\\ \\frac{dm}{dt} \\end{array}\\right]$\n",
"\n",
"Use [two integration methods](../notebooks/03_Get_Oscillations.ipynb) to integrate the `rocket` function, one explicit method and one implicit method. Demonstrate that the solutions converge to equation (2.b) the Tsiolkovsky equation. Use an initial state of y=0 m, v=0 m/s, and m=0.25 kg. \n",
"\n",
"Integrate the function until mass, $m_{f}=0.05~kg$, using a mass rate change of $\\frac{dm}{dt}=0.05$ kg/s, . \n",
"\n",
"Compare solutions between the `simplerocket` and `rocket` integration, what is the height reached when the mass reaches $m_{f} = 0.05~kg?$\n"
]
},
{
"cell_type": "code",
"execution_count": 316,
"metadata": {},
"outputs": [],
"source": [
"def rocket(state,dmdt=0.05, u=250,c=0.18e-3,g=9.81):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, with drag, in SI units.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" c : drag constant for a rocket set to 0.18e-3 kg/m\n",
" Returns\n",
" -------\n",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" dstate = np.array([state[1], (u/state[2])*dmdt - g - (c/state[2])*(state[1]**2), -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Runge Kutta Two Step**"
]
},
{
"cell_type": "code",
"execution_count": 317,
"metadata": {},
"outputs": [],
"source": [
"#initialize solution array\n",
"sol2_rk2 = np.zeros([N,3])\n",
"\n",
"sol2_rk2[0,0] = y0\n",
"sol2_rk2[0,1] = v0\n",
"sol2_rk2[0,2] = m0\n",
"\n",
"#Integration using Explicit Method: Modified Euler Runge Kutta two step\n",
"for i in range(N-1):\n",
" sol2_rk2[i+1] = rk2_step(sol2_rk2[i], rocket, dt)\n",
"\n",
"mt2_rk2 = sol2_rk2[:,2]/m0\n",
"v2_rk2 = sol2_rk2[:,1]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Analytical**"
]
},
{
"cell_type": "code",
"execution_count": 318,
"metadata": {},
"outputs": [],
"source": [
"# Anlytical Solution: Tsiokovsky Solution\n",
"mt = np.linspace(m0,mf,N+1)\n",
"dm = mt/m0\n",
"vf = -250*np.log(dm)"
]
},
{
"cell_type": "code",
"execution_count": 319,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(dm, vf, label=\"Tsiokovsky Solution\", linestyle ='dashed')\n",
"plt.plot(mt2_rk2, v2_rk2, label=\"Runge Kutta\")\n",
"\n",
"plt.title(\"Simplerocket Mass Ratio vs. Velocity\")\n",
"plt.xlabel(\"mf/m0 [kg]\")\n",
"plt.ylabel(\"Velocity [m/s]\")\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Heun's Method**"
]
},
{
"cell_type": "code",
"execution_count": 320,
"metadata": {},
"outputs": [],
"source": [
"#initialize solution array\n",
"sol2_heun = np.zeros([N,3])\n",
"\n",
"sol2_heun[0,0] = y0\n",
"sol2_heun[0,1] = v0\n",
"sol2_heun[0,2] = m0\n",
"\n",
"#Integration using Implicit Method: Heun Step\n",
"for i in range(N-1):\n",
" sol2_heun[i+1] = heun_step(sol2_heun[i], rocket, dt)\n",
"\n",
"mt2_heun = sol2_heun[:,2]/m0\n",
"v2_heun = sol2_heun[:,1]"
]
},
{
"cell_type": "code",
"execution_count": 321,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(dm, vf, label=\"Tsiokovsky Solution\")\n",
"plt.plot(mt2_heun, v2_heun, label=\"Heun\", linestyle = 'dashed')\n",
"\n",
"plt.title(\"Simplerocket Mass Ratio vs. Velocity\")\n",
"plt.xlabel(\"mf/m0 [kg]\")\n",
"plt.ylabel(\"Velocity [m/s]\")\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Height Comparison**"
]
},
{
"cell_type": "code",
"execution_count": 322,
"metadata": {},
"outputs": [],
"source": [
"simpleRocket_rk2_h = sol_rk2[:,0]\n",
"simpleRocket_heun_h = sol_heun[:,0]\n",
"rocket_rk2_h = sol2_rk2[:,0]\n",
"rocket_heun_h = sol2_heun[:,0]"
]
},
{
"cell_type": "code",
"execution_count": 323,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t, simpleRocket_rk2_h, label=\"Simple Rocket \", linestyle ='dashed')\n",
"plt.plot(t, rocket_rk2_h, label=\"Rocket\")\n",
"plt.title(\"Runge Kutta Heights\")\n",
"plt.xlabel(\"time [s]\")\n",
"plt.ylabel(\"Height [m]\")\n",
"plt.legend(loc ='best');"
]
},
{
"cell_type": "code",
"execution_count": 324,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t, simpleRocket_heun_h, label=\"Simple Rocket \", linestyle ='dashed')\n",
"plt.plot(t, rocket_heun_h, label=\"Rocket\")\n",
"plt.title(\"Heun Heights\")\n",
"plt.xlabel(\"time [s]\")\n",
"plt.ylabel(\"Height [m]\")\n",
"plt.legend(loc ='best');"
]
},
{
"cell_type": "code",
"execution_count": 325,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The final heights using the Simple Rocket Function are 597.24 m and 597.96 m using RK2 and Heuns method respectively\n",
"The final heights using the Rocket Function are 425.43 m and 425.44 m using RK2 and Heuns method respectively\n"
]
}
],
"source": [
"print('The final heights using the Simple Rocket Function are {:.2f} m and {:.2f} m using RK2 and Heuns method respectively'.format(simpleRocket_rk2_h[-1],simpleRocket_heun_h[-1]) )\n",
"print('The final heights using the Rocket Function are {:.2f} m and {:.2f} m using RK2 and Heuns method respectively'.format(rocket_rk2_h[-1], rocket_heun_h[-1]) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3. Solve for the mass change rate that results in detonation at a height of 300 meters. Create a function `f_dm` that returns the final height of the firework when it reaches $m_{f}=0.05~kg$. The inputs should be \n",
"\n",
"$f_{m}= f_{m}(\\frac{dm}{dt},~parameters)$\n",
"\n",
"where $\\frac{dm}{dt}$ is the variable we are using to find a root and $parameters$ are the known values, `m0=0.25, c=0.18e-3, u=250`. When $f_{m}(\\frac{dm}{dt}) = 0$, we have found the correct root. \n",
"\n",
"Plot the height as a function of time and use a star to denote detonation at the correct height with a `'*'`-marker\n",
"\n",
"Approach the solution in two steps, use the incremental search [`incsearch`](../notebooks/04_Getting_to_the_root.ipynb) with 5-10 sub-intervals _we want to limit the number of times we call the function_. Then, use the modified secant method to find the true root of the function.\n",
"\n",
"a. Use the incremental search to find the two closest mass change rates within the interval $\\frac{dm}{dt}=0.05-0.4~kg/s.$\n",
"\n",
"b. Use the modified secant method to find the root of the function $f_{m}$.\n",
"\n",
"c. Plot your solution for the height as a function of time and indicate the detonation with a `*`-marker."
]
},
{
"cell_type": "code",
"execution_count": 386,
"metadata": {},
"outputs": [],
"source": [
"def f_m(dmdt,m0=0.25,mf =0.05,c=0.18e-3,u=250,g=9.81):\n",
" ''' define a function f_m(dmdt) that returns \n",
" height_desired-height_predicted[-1]\n",
" here, the time span is based upon the value of dmdt\n",
" \n",
" arguments:\n",
" ---------\n",
" dmdt: the unknown mass change rate\n",
" m0: the known initial mass\n",
" c: the known drag in kg/m\n",
" u: the known speed of the propellent\n",
" \n",
" returns:\n",
" --------\n",
" error: the difference between height_desired and height_predicted[-1]\n",
" when f_m(dmdt)= 0, the correct mass change rate was chosen\n",
" '''\n",
" \n",
" #set initial conditions\n",
" y_0 = 0\n",
" v_0 = 0 \n",
" \n",
" # initialize array\n",
" \n",
" tf = (m0-mf)/dmdt\n",
" t=np.linspace(0,tf,1000)\n",
" dt=t[1]-t[0]\n",
" N = int(tf/dt)\n",
" \n",
" # Set intial conditions\n",
" num_sol = np.zeros([N,3])\n",
" num_sol[0,0] = y0\n",
" num_sol[0,1] = v0\n",
" num_sol[0,2] = m0\n",
"\n",
" for i in range(N-1):\n",
" num_sol[i+1] = rk2_step(num_sol[i], lambda state: rocket(state,dmdt=dmdt) ,dt)\n",
" \n",
" \n",
" h_desired = 300\n",
" height = num_sol[-1,0]\n",
" \n",
" error = h_desired - height\n",
" \n",
" return error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Part A: IncSearch**"
]
},
{
"cell_type": "code",
"execution_count": 377,
"metadata": {},
"outputs": [],
"source": [
"def incsearch(func,xmin,xmax,ns=50):\n",
" '''incsearch: incremental search root locator\n",
" xb = incsearch(func,xmin,xmax,ns):\n",
" finds brackets of x that contain sign changes\n",
" of a function on an interval\n",
" arguments:\n",
" ---------\n",
" func = name of function\n",
" xmin, xmax = endpoints of interval\n",
" ns = number of subintervals (default = 50)\n",
" returns:\n",
" ---------\n",
" xb(k,1) is the lower bound of the kth sign change\n",
" xb(k,2) is the upper bound of the kth sign change\n",
" If no brackets found, xb = [].'''\n",
" \n",
" x = np.linspace(xmin,xmax,ns)\n",
" f = np.zeros(ns)\n",
" #modifying the function to allow an array to pass through the function\n",
" for i in range(ns):\n",
" f[i]=func(x[i])\n",
" sign_f = np.sign(f)\n",
" delta_sign_f = sign_f[1:]-sign_f[0:-1]\n",
" i_zeros = np.nonzero(delta_sign_f!=0)\n",
" nb = len(i_zeros[0])\n",
" xb = np.block([[ x[i_zeros[0]+1]],[x[i_zeros[0]] ]] )\n",
" if nb==0:\n",
" print('no brackets found\\n')\n",
" print('check interval or increase ns\\n')\n",
" else:\n",
" print('number of brackets: {}\\n'.format(nb))\n",
" return xb"
]
},
{
"cell_type": "code",
"execution_count": 378,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n",
"The range of values for dmdt is between 0.08571428571428572 kg/s and 0.07857142857142857 kg/s using IncSearch\n"
]
}
],
"source": [
"xmin = 0.05\n",
"xmax = 0.4\n",
"x = np.linspace(xmin,xmax)\n",
"change_rate = incsearch(f_m,xmin,xmax)\n",
"dmdt_ub = np.float(change_rate[0]) \n",
"dmdt_lb = np.float(change_rate[1])\n",
"\n",
"\n",
"print('The range of values for dmdt is between {} kg/s and {} kg/s using IncSearch'.format(dmdt_ub,dmdt_lb)); "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Part B: ModSecant**"
]
},
{
"cell_type": "code",
"execution_count": 379,
"metadata": {},
"outputs": [],
"source": [
"def mod_secant(func,dx,x0,es=0.0001,maxit=50):\n",
" '''mod_secant: Modified secant root location zeroes\n",
" root,[fx,ea,iter]=mod_secant(func,dfunc,xr,es,maxit,p1,p2,...):\n",
" uses modified secant method to find the root of func\n",
" arguments:\n",
" ----------\n",
" func = name of function\n",
" dx = perturbation fraction\n",
" x0 = initial guess\n",
" es = desired relative error (default = 0.0001 )\n",
" maxit = maximum allowable iterations (default = 50)\n",
" p1,p2,... = additional parameters used by function\n",
" returns:\n",
" --------\n",
" root = real root\n",
" fx = func evaluated at root\n",
" ea = approximate relative error ( )\n",
" iter = number of iterations'''\n",
"\n",
" iter = 0;\n",
" xr=x0\n",
" for iter in range(0,maxit):\n",
" xrold = xr;\n",
" dfunc=(func(xr+dx)-func(xr))/dx;\n",
" xr = xr - func(xr)/dfunc;\n",
" if xr != 0:\n",
" ea = abs((xr - xrold)/xr) * 100;\n",
" else:\n",
" ea = abs((xr - xrold)/1) * 100;\n",
" if ea <= es:\n",
" break\n",
" return xr,[func(xr),ea,iter]\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 380,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.08571428571428572"
]
},
"execution_count": 380,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dmdt_ub"
]
},
{
"cell_type": "code",
"execution_count": 387,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The root of the function f_m is 0.07890352691867966 using ModSecant\n"
]
}
],
"source": [
"root, out = mod_secant(f_m, 0.0001,dmdt_ub,es=.000001)\n",
"print(\"The root of the function f_m is {} using ModSecant\".format(root))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Part C: Plot**"
]
},
{
"cell_type": "code",
"execution_count": 399,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"dmdt_final = root\n",
"h_desired = 300\n",
"\n",
"tf = (m0-mf)/dmdt\n",
"t = np.linspace(0,tf,10000)\n",
"dt = t[1] - t[0]\n",
" \n",
"N = int(tf/dt)\n",
"t_final = np.linspace(0,tf,N)\n",
"\n",
"#initialize solution array\n",
"height = np.zeros([N,3])\n",
"\n",
"#Set intial conditions\n",
"height[0,0] = y0\n",
"height[0,1] = v0\n",
"height[0,2] = m0\n",
"\n",
"for i in range(N-1):\n",
" height[i+1] = rk2_step(height[i],lambda state: rocket(state,dmdt=dmdt_final,u=250),dt)\n",
"\n",
"\n",
"plt.plot(t_final[-1],h_desired,'*',label='300 meters');\n",
"plt.plot(t_final,height[:,0],'k:');\n",
"plt.title('Height v Time');\n",
"plt.xlabel('time (s)');\n",
"plt.ylabel('height (m)');\n",
"plt.grid(True);\n",
"plt.legend();\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## References\n",
"\n",
"1. Math 24 _Rocket Motion_. <https://www.math24.net/rocket-motion/\\>\n",
"\n",
"2. Kasdin and Paley. _Engineering Dynamics_. [ch 6-Linear Momentum of a Multiparticle System pp234-235](https://www.jstor.org/stable/j.ctvcm4ggj.9) Princeton University Press \n",
"\n",
"3. <https://en.wikipedia.org/wiki/Specific_impulse>\n",
"\n",
"4. <https://www.apogeerockets.com/Rocket_Motors/Estes_Motors/13mm_Motors/Estes_13mm_1_4A3-3T>"
]
}
],
"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": 4
}