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Planar Launch State Equations.ipynb
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"# ENAE 791 Launch Dynamics\n",
"## Planar State Equations for Ascending Launch Vehicles\n",
"\n",
"This document contains notes from the April 26 lecture - _Launch Planar State Equations_. The planar launch state equations were also coded in Python below."
]
},
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"source": [
"# Imports for Python code below\n",
"from scipy.integrate import solve_ivp\n",
"\n",
"import numpy as np\n",
"import scipy as sci\n",
"import astropy as astro\n",
"\n",
"import astropy.units as units\n",
"\n",
"import matplotlib.pyplot as plt\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
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"### Accelerations Relative to $\\bar{V}$\n",
"\n",
"#### Acceleration (thrust and normal components)\n",
"$$ a_T = \\dot{V} = \\frac{F_T}{m} $$ \n",
"\n",
"$$ a_N = V(\\dot{\\gamma} - \\dot{\\theta}) = \\frac{F_N}{m} $$ \n",
"\n",
"#### Change in true anomoly, altitude\n",
"$$ \\dot{\\theta} = \\frac{V \\cos{\\gamma}}{r} $$ \n",
"\n",
"$$ \\dot{r} = \\dot{h} = V \\sin{\\gamma} $$ \n",
"\n",
"#### Change in velocity\n",
"$$\n",
" \\begin{align*}\n",
" \\dot{V} = &+\\frac{\\mu \\sin{\\gamma}}{r^2} &\\text{(gravity term)} \\\\\n",
" &- \\frac{D}{m} &\\text{(drag term)} \\\\\n",
" &+ \\frac{T}{m}\\cos{\\gamma} &\\text{(control inputs)}\n",
" \\end{align*}\n",
"$$\n",
"\n",
"#### Change in flight path angle \n",
"$$\n",
" \\begin{align*}\n",
" \\dot{\\gamma} = &-\\frac{\\mu \\cos{\\gamma}}{v r^2} \\ \\ \\ &\\text{(gravity term)} \\\\\n",
" &- \\frac{L}{V m} \\ \\ \\ &\\text{(lift term)} \\\\\n",
" &+ \\frac{V \\cos{\\gamma}}{r} \\ \\ \\ &\\text{(change in true anomoly, }\\dot{\\theta}\\text{)} \\\\\n",
" &+ \\frac{T}{V m} \\sin{\\phi} \\ \\ \\ &\\text{(control inputs)}\n",
" \\end{align*}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Planar State Equation Derivation\n",
"We have two control inputs: \n",
"\n",
"1. $ T \\ \\ \\ \\text{(thrust)} $ \n",
"2. $ \\phi \\ \\ \\ \\text{(Thrust Direction, angle between thrust vector and velocity vector)} $ \n",
"\n",
"The planar dynamical equations are shown below:\n",
"\n",
"$$ \n",
" \\begin{align*}\n",
" \\dot{V} &= - \\frac{\\mu \\sin{\\gamma}}{r^2} - \\frac{1}{2}\\rho v^2 \\frac{A C_D}{m} + \\frac{T}{m}\\cos{\\phi} \\\\ \\\\\n",
" \\dot{\\gamma} &= -\\frac{\\mu \\cos{\\gamma}}{r^2} + \\frac{1}{2} \\rho v^2 \\frac{A C_D}{m} \\frac{L}{D} + v \\frac{\\cos{\\gamma}}{r} + \\frac{T}{V m} \\sin{\\phi} \\\\ \\\\\n",
" \\dot{\\theta} &= v \\frac{\\cos{\\gamma}}{r} \\\\ \\\\\n",
" \\dot{r} &= \\dot{h} = v \\sin{\\gamma} \\\\ \\\\\n",
" \\dot{m} &= -\\frac{T}{V_e} \n",
" \\end{align*}\n",
"$$ "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Planar State Equations\n",
"\n",
"Define the following state and input variables:\n",
"\n",
"$$ \n",
" x = \\begin{bmatrix} v \\\\ \\gamma \\\\ \\theta \\\\ r \\\\ m \\end{bmatrix} \n",
" = \\begin{bmatrix} x_1 \\\\ x_2 \\\\ x_3 \\\\ x_4 \\\\ x_5 \\end{bmatrix}\n",
"$$\n",
"\n",
"$$ \n",
" u = \\begin{bmatrix} T \\\\ \\phi \\end{bmatrix} = \\begin{bmatrix} u_1 \\\\ u_2 \\end{bmatrix}\n",
"$$\n",
"\n",
"The Planar Launch State Equations are shown below:\n",
"\n",
"$$ \n",
" \\dot{x} = f(x,u) = \\begin{bmatrix} \n",
" -\\frac{\\mu \\sin{x_2}}{x_3^2} - \\frac{1}{2}\\frac{\\rho x_1^2 c_D A}{x_5} + \\frac{u_1}{x_5}\\cos{u_2} \\\\\n",
" -\\frac{\\mu \\cos{x_2}}{x_3^2} + \\frac{L}{x_1 x_5} + \\frac{x_1 \\cos{x_2}}{x_3} + \\frac{u_1}{x_1 x_5}\\sin{u_2} \\\\\n",
" x_1 \\frac{\\cos{x_2}}{x_3} \\\\\n",
" x_1 \\sin{x_2} \\\\\n",
" -\\frac{u_1}{V_e}\n",
" \\end{bmatrix}\n",
"$$\n",
"\n"
]
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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"def impact_ground(t,y):\n",
" return y[3] - astro.constants.R_earth.to('m').value\n",
"impact_ground.terminal = True\n",
"\n",
"def planarLaunchDynamicsTic(t, z, _u, _mu, _c_D, _L_D, _A, _V_e, _h_s, _rho_0, _r_0):\n",
" v = z[0]\n",
" gamma = z[1]\n",
" theta = z[2]\n",
" r = z[3]\n",
" m = z[4]\n",
" u1 = _u[0]\n",
" u2 = _u[1]\n",
" \n",
" # Altitude\n",
" h = r - _r_0\n",
" \n",
" # Air density at altitude\n",
" rho = _rho_0 * np.exp(-h / _h_s)\n",
"\n",
" return [\n",
" -(_mu * np.sin(gamma) / (r**2)) - ((rho/2) * v**2 * _c_D * _A / m) + (u1 * np.cos(u2) / m),\n",
" -(_mu * np.cos(gamma) / (r**2)) + (v * np.cos(gamma) / r) + (u1 * np.sin(u2) / (v*m)),\n",
" v * np.cos(gamma) / r,\n",
" v * np.sin(gamma),\n",
" -u1 / _V_e\n",
" ]\n",
"\n",
"traj = solve_ivp(\n",
" lambda t,z : planarLaunchDynamicsTic(\n",
" t,z,\n",
" _u=\n",
" [\n",
" 1e6, # thrust input\n",
" 0 # thrust direction input\n",
" ],\n",
" _mu=astro.constants.GM_earth.to('m^3/s^2').value,\n",
" _c_D=1.2,\n",
" _L_D = 0.25,\n",
" _A=20,\n",
" _V_e=4200,\n",
" _h_s=7524,\n",
" _rho_0=1.225,\n",
" _r_0=astro.constants.R_earth.to('m').value\n",
" ),\n",
" [ ## Time window for solve_ivp\n",
" 0, # start_time\n",
" 100 # end_time \n",
" ],\n",
" [ ## Initial Conditions for solve_ivp\n",
" 17000, # V0\n",
" 0.25, # gamma0\n",
" 0, # theta0\n",
" 100 + astro.constants.R_earth.to('m').value, # r0\n",
" 350000 # m0\n",
" ],\n",
" events=impact_ground, # Link with landing event\n",
" t_eval=np.linspace(0, 100, int(1e6)) * units.s # Sim evaluation times\n",
")\n",
"\n",
"plt.figure()\n",
"plt.plot(traj.t, traj.y[3]*units.m - astro.constants.R_earth)\n",
"plt.title('Altitude vs. Time')\n",
"plt.ylabel('Altitude (m)')\n",
"plt.xlabel('Time (s)')\n",
"plt.show();\n",
"\n",
"plt.figure()\n",
"plt.plot(traj.t, (traj.y[0]*units.m/units.s).to('km/hr'))\n",
"plt.title('Velocity vs. Time')\n",
"plt.ylabel('Velocity (km/hr)')\n",
"plt.xlabel('Time (s)')\n",
"plt.show();\n",
"\n",
"plt.figure()\n",
"plt.plot(traj.t, (traj.y[1]*units.rad).to('deg'))\n",
"plt.title('Gamma vs. Time')\n",
"plt.ylabel('Gamma (deg)')\n",
"plt.xlabel('Time (s)')\n",
"plt.show();\n",
"\n",
"plt.figure()\n",
"plt.plot(traj.t, (traj.y[2]*units.rad).to('deg'))\n",
"plt.title('Theta vs. Time')\n",
"plt.ylabel('Theta (rad)')\n",
"plt.xlabel('Time (s)')\n",
"plt.show();\n",
"\n",
"plt.figure()\n",
"plt.plot(traj.t, (traj.y[4]*units.kg).to('t'))\n",
"plt.title('Mass vs. Time')\n",
"plt.ylabel('Mass (tonne)')\n",
"plt.xlabel('Time (s)')\n",
"plt.show();"
]
}
],
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@cadojo
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cadojo commented Jun 19, 2020

Current Issues

If you take a look at the plots, that doesn't look like a launch! There are at least one of the following two issues:

  1. Some part of the planar launch state equations are incorrect

  2. There is some bug, or typo in the propagator code

To do

  • Double check the planar state equations, make sure simple things make sense (sum of forces, correct signs, etc.)

  • Double check the propagator code for any typos, make sure that the dynamics in the code match the equations

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