{ "cells": [ { "cell_type": "code", "execution_count": 4, "id": "bec17a8e", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import quad" ] }, { "cell_type": "markdown", "id": "83411453-6cde-4a2f-ad1c-833ac21554d2", "metadata": {}, "source": [ "
Use scipy.integrate.quad to evaluate the following definite integrals (which can also be expressed in closed form over the range given but are awkward).
\n", "$$\n", "\\int_0^1 \\frac{x^4(1-x)^4}{1+x^2}\\;\\mathrm{d}x.\n", "$$\n", "(Compare with $22/7 - \\pi$).
\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "170e08b6-75ee-4bd5-92f9-d6b0095a7fdc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0.0012644892673496185, 1.1126990906558069e-14)\n", "0.0012644892673496777\n" ] } ], "source": [ "f1 = lambda x: x**4 * (1 - x)**4/(1 + x**2)\n", "print(quad(f1, 0, 1))\n", "print(22/7 - np.pi)" ] }, { "cell_type": "markdown", "id": "c7177654-38f9-41ce-8bde-8e58202cfbbc", "metadata": {}, "source": [ "The following integral appears in the Debye theory of the heat capacity of crystals at low temperature\n", "$$\n", "\\int_0^\\infty \\frac{x^3}{e^x-1}\\;\\mathrm{d}x\n", "$$\n", "(Compare with $\\pi^4/15$).
\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "189c630d-d033-450e-ac6f-41f697d4abef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(6.49393940226683, 2.628470027132503e-09)\n", "6.493939402266828\n" ] } ], "source": [ "f2 = lambda x: x**3/(np.exp(x) - 1)\n", "\n", "print(quad(f2, 0, np.inf))\n", "print(np.pi**4/15)" ] }, { "cell_type": "markdown", "id": "1b97ab5b-9482-4cf6-b117-add283248804", "metadata": {}, "source": [ "The integral sometimes known as the Sophomore's dream:\n", "$$\n", "\\int_0^1 x^{-x}\\;\\mathrm{d}x\n", "$$\n", "(Compare the value you obtain from the summation $\\sum_{n=1}^\\infty n^{-n}$).
" ] }, { "cell_type": "code", "execution_count": 7, "id": "d9615549-1562-4536-ab28-e4e556e025d3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1.2912859970626633, 3.668398917966442e-11)\n", "1.2912859970626636\n" ] } ], "source": [ "f3 = lambda x: x**-x\n", "\n", "print(quad(f3, 0, 1))\n", "\n", "n, I, TOL = 0, 0, 1.e-16\n", "while True:\n", " Iold = I\n", " n += 1\n", " I += n**-n\n", " if I-Iold < TOL:\n", " break\n", "\n", "print(I)" ] }, { "cell_type": "markdown", "id": "fd89ea5d-e024-4718-a7ae-6cd2d479f961", "metadata": {}, "source": [ "\n", "$$\n", "\\int_0^1 [\\ln(1/x)]^p\\;\\mathrm{d}x\n", "$$\n", "(Compare with $p!$ for integer $0 \\le p \\le 10$).
\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "558a4a0e-653e-4aef-ace3-6dff92535b58", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0 1.0\n", "0.9999999999999999 1.0\n", "1.9999999999999978 2.0\n", "5.999999999999848 6.0\n", "23.99999999999799 24.0\n", "120.0000000000472 120.0\n", "719.9999999995489 720.0\n", "5040.000000415095 5040.0\n", "40320.000004345224 40320.0\n", "362880.0000102735 362880.0\n" ] } ], "source": [ "from scipy.special import factorial\n", "f4 = lambda x, p: np.log(1/x)**p\n", "for p in range(10):\n", " print(quad(f4, 0, 1, args=(p,))[0], factorial(p))" ] }, { "cell_type": "markdown", "id": "0efe3dff-4798-4882-bab0-944416f2a174", "metadata": {}, "source": [ "\n", "$$\n", "\\int_0^{2\\pi} e^{z\\cos\\theta}\\;\\mathrm{d}\\theta\n", "$$\n", "(Compare with $2\\pi I_0(z)$, where $I_0(z)$ is a modified Bessel function of the first kind, for $0 \\le z \\le 2$).\n", "Here we find the maximum deviation from the Bessel function $I_0(z)$\n", " for 100 values of $z$\n", " between 0 and 2:\n", "
" ] }, { "cell_type": "code", "execution_count": 9, "id": "2abfd3c9-3455-4a9e-9942-abc4a03da661", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.4796610037801656e-12\n" ] } ], "source": [ "from scipy.special import i0\n", "z = np.linspace(0,2,100)\n", "y1 = i0(z)\n", "f5 = lambda theta, z: np.exp(z*np.cos(theta))\n", "y2 = np.array([quad(f5, 0, 2*np.pi, args=(zz,))[0] for zz in z])\n", "y2 /= 2 * np.pi\n", "print(np.max(abs(y2-y1)))" ] }, { "cell_type": "markdown", "id": "77ca028b-d060-4a6d-b253-e03bf7e4e677", "metadata": {}, "source": [ "\n", "---\n", "\n", "The trajectory of a projectile in the $xz$-plane launched from the origin at an angle $\\theta_0$ from the (horizontal) $x$-axis with speed $v_0 = 25\\;\\mathrm{m\\,s^{-1}}$ is\n", "$$\n", "z = x\\tan\\theta_0 - \\frac{g}{2v_0^2\\cos^2\\theta_0}x^2.\n", "$$
\n", "\n", "During its flight, the projectile is subject to a constant acceleration $\\ddot{\\boldsymbol{r}} = -g\\hat{\\boldsymbol{k}}$. Integrating,\n", "$$\n", "\\begin{align*}\n", "\\boldsymbol{v} = \\dot{\\boldsymbol{r}} = -gt\\hat{\\boldsymbol{k}} + \\boldsymbol{v_0}\\\\\n", "\\boldsymbol{r} = \\textstyle -\\frac{1}{2}gt^2\\hat{\\boldsymbol{k}} + \\boldsymbol{v_0}t + \\boldsymbol{r_0}\n", "\\end{align*}\n", "$$\n", "where $\\boldsymbol{v_0} = (v_0\\cos\\theta)\\hat{\\boldsymbol{i}} + v_0(\\sin\\theta)\\hat{\\boldsymbol{k}}$ and $\\boldsymbol{r_0}=0$ (the projectile starts at the origin).\n", "\n", "Therefore, $x = v_0t\\cos\\theta$ and $z = v_0t\\sin\\theta - \\frac{1}{2}gt^2$. Eliminating $t$ from these expressions gives the formula for $z$ above.\n", "\n", "\n", "If the projectile passes through the point $(5, 15)$, use Brent's method to determine the possible values of $\\theta_0$.
\n", "\n", "In general, there are two (physically distinct) possible angles $\\theta_0$ corresponding to the projectile passing through the specified point, $(x_1, y_1) = (5,15)$, on the way up or on the way down. These values are the roots in $(0, \\pi/2)$ of the function\n",
"$$\n",
"f(\\theta_0; x_1, z_1) = x_1\\tan\\theta_0 - \\frac{g x_1^2}{2v_0^2\\cos^2\\theta_0} - z_1\n",
"$$\n",
"After bracketing the roots with a rough plot of $f(\\theta_0)$, we can use brentq:
That is, $\\theta_0 = 74.2^\\circ$ or $\\theta_0 = 87.4^\\circ$.
" ] }, { "cell_type": "markdown", "id": "7e678173-3941-43b3-8f48-6f75adde3178", "metadata": {}, "source": [ "\n", "---\n", "\n", "A spherical projectile of mass $m$ launched with some initial velocity moves under the influence of two forces: gravity, $\\boldsymbol{F}_g = -mg\\boldsymbol{\\hat{z}}$, and air resistance (drag), $\\boldsymbol{F}_D = -\\frac{1}{2}c\\rho A v^2 \\boldsymbol{v}/|\\boldsymbol{v}| = -\\frac{1}{2}c\\rho A v\\boldsymbol{v}$, acting in the opposite direction to the projectile's velocity and proportional to the square of that velocity (under most realistic conditions). Here, $c$ is the drag coefficient, $\\rho$ the air density, and $A$ the projectile's cross-sectional area.
\n", "The relevant equations of motion are therefore:\n",
"$$\n",
"\\begin{align*}\n",
"m\\ddot{x} = -k\\sqrt{\\dot{x}^2 + \\dot{z}^2}\\dot{x},\\\\\n",
"m\\ddot{z} = -k\\sqrt{\\dot{x}^2 + \\dot{z}^2}\\dot{z} - mg,\n",
"\\end{align*}\n",
"$$\n",
"where $v = |\\boldsymbol{v}| = \\sqrt{\\dot{x}^2 + \\dot{z}^2}$ and $k=\\frac{1}{2}c\\rho A$. These can be decomposed into the following four first-order ODEs with $u_1 \\equiv x, u_2 \\equiv \\dot{x}, u_3 \\equiv z, u_4 \\equiv \\dot{z}$:\n",
"$$\n",
"\\begin{align*}\n",
"\\dot{u}_1 = u_2,\\\\\n",
"\\dot{u}_2 = -\\frac{k}{m}\\sqrt{u_2^2 + u_4^2}u_2,\\\\\n",
"\\dot{u}_3 = u_4, \\\\\n",
"\\dot{u}_4 = -\\frac{k}{m}\\sqrt{u_2^2 + u_4^2}u_4 - g.\n",
"\\end{align*}\n",
"$$\n",
"The following code integrates this system and identifies two events: hitting the target (the projectile returning to the ground at $z=0$) and reaching its maximum height (at which the z-component of its velocity is zero). We set the additional attribute hit_target.direction = -1 to ensure that hit_target only triggers the event when its return value (the projectile's elevation) goes from positive to negative; otherwise the event would be triggered at launch since $z_0 = 0$. Other possibilities are direction = 1: trigger the event when the return value changes from negative to positive or direction = 0 (the default): the event is triggered when the return value is zero from either direction.
The provided second-order differential equation can, in fact, be wrangled into a single first-order differential equation but we choose here to reduce it to two such equations in variables $\\theta$ and $\\dot{\\theta}$:\n", "\\begin{align*}\n", "\\frac{\\mathrm{d}\\dot{\\theta}}{\\mathrm{d}t} = -\\frac{g}{l}\\sin\\theta,\\\\\n", "\\frac{\\mathrm{d}\\theta}{\\mathrm{d}t} = \\dot{\\theta}.\n", "\\end{align*}
" ] }, { "cell_type": "code", "execution_count": 14, "id": "bd3a9235-6dbd-40c8-a698-03e0b3384d9d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Let the centre of the small circle be $(r, b)$ (the $x$-coordinate of its centre must be $r$ because it is tangent to the $y$-axis. The equation of this circle is therefore
\n", "$$\n", "(x-r)^2 + (y-b)^2 = r^2\n", "$$
\n", "At the point $Q$ the small circle is tangent to the unit circle: let $Q=(d, \\sqrt{1-d^2})$, where:
\n", "$$\n", "(d-r)^2 + \\left[\\sqrt{1-d^2} - b\\right]^2 = r^2\n", "$$
\n", "The gradients of the purple and orange curves are:
\n", "\\begin{align}\n", "y' = \\frac{-x}{\\sqrt{1-x^2}}\\\\\n", "2(x-r) + 2(y-b)y' = 0 \\Rightarrow y' = \\frac{r-x}{y-b}.\n", "\\end{align}
\n", "and these are equal at $x=d$, so
\n", "$$\n", "d\\left[\\sqrt{1-d^2}-b\\right] = (d-r)\\sqrt{1-d^2}.\n", "$$
\n", "SymPy can solve this pair of equations for $d$ and $r$ in terms of (the still unknown) $b$ straight away:
" ] }, { "cell_type": "code", "execution_count": 2, "id": "88f7a0a1-5016-4c0a-839b-5126441ee4bc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[{d: sqrt(b**4 - 2*b**2 + 1)/(b**2 + 1), r: sqrt(b**4 - 2*b**2 + 1)/2}]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy as sp\n", "r, b, c, d = sp.symbols(\"r b c d\", positive=True, real=True)\n", "E1 = (d - r)**2 + (sp.sqrt(1 - d**2) - b)**2 - r**2\n", "E2 = d * (sp.sqrt(1 - d**2) - b) - (d - r) * sp.sqrt(1 - d**2)\n", "soln1 = sp.solve([E1, E2], [r, d], dict=True)\n", "soln1" ] }, { "cell_type": "markdown", "id": "451b4f61-4bde-41fa-a72a-bbc802ba3317", "metadata": {}, "source": [ "That is,\n", "$$\n", "d = \\frac{\\sqrt{b^4-2b^2+1}}{b^2+1}, \\; r = \\frac{1}{2}\\sqrt{b^4-2b^2+1}.\n", "$$
\n", "At the point $P$ the small circle is tangent to the curve $y=\\sqrt{x}$. Let $P=(c,\\sqrt{c})$, so
\n", "$$\n", "(c-r)^2+\\left(\\sqrt{c}-b\\right)^2 = r^2\n", "$$
\n", "and from the gradient of the red line,
\n", "$$\n", "y' = \\frac{1}{2\\sqrt{x}}\n", "$$
\n", "at $x=c$ we have
\n", "$$\n", "\\frac{1}{2\\sqrt{c}} = \\frac{r-c}{\\sqrt{c}-b} \\Rightarrow \\sqrt{c} - b = 2\\sqrt{c}(r-c).\n", "$$
\n", "This pair of equations can also be solved (for $b$ and $c$)
" ] }, { "cell_type": "code", "execution_count": 3, "id": "12796197-d26f-4b5b-9d86-b168744737df", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[{b: (3/16 - sqrt(16*r + 1)/16)*sqrt(16*r - 2*sqrt(16*r + 1) - 2),\n", " c: r - sqrt(16*r + 1)/8 - 1/8},\n", " {b: (sqrt(16*r + 1)/16 + 3/16)*sqrt(16*r + 2*sqrt(16*r + 1) - 2),\n", " c: r + sqrt(16*r + 1)/8 - 1/8}]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E3 = (c - r)**2 + (sp.sqrt(c) - b)**2 - r**2\n", "E4 = sp.sqrt(c) - b - 2 * sp.sqrt(c) * (r - c)\n", "soln2 = sp.solve([E3, E4], [b, c], dict=True)\n", "soln2" ] }, { "cell_type": "markdown", "id": "088e1246-4a36-436c-a7ef-6852d348b1c1", "metadata": {}, "source": [ "This time there are two solutions (equations for $b$ in terms of $r$), and solving each of these gives a total of four equations for $r$:
" ] }, { "cell_type": "code", "execution_count": 4, "id": "cab1bc44-3cdf-4e83-ac4e-ba1d70f39aa9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1/2,\n", " 11/8 + sqrt(227/(96*(251*sqrt(3765)/9216 + 2159/1024)**(1/3)) + 2*(251*sqrt(3765)/9216 + 2159/1024)**(1/3) + 145/16)/2 + sqrt(-2*(251*sqrt(3765)/9216 + 2159/1024)**(1/3) - 227/(96*(251*sqrt(3765)/9216 + 2159/1024)**(1/3)) + 1631/(32*sqrt(227/(96*(251*sqrt(3765)/9216 + 2159/1024)**(1/3)) + 2*(251*sqrt(3765)/9216 + 2159/1024)**(1/3) + 145/16)) + 145/8)/2]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b1 = soln2[0][b]\n", "r1 = sp.solve(soln1[0][r].subs(b, b1) - r, r)\n", "r1" ] }, { "cell_type": "code", "execution_count": 5, "id": "ed065fab-50dd-4665-97e5-6cb89b0bc5c7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[-1 - 25/(12*(75/16 + 175*sqrt(21)/144)**(1/3)) + (75/16 + 175*sqrt(21)/144)**(1/3),\n", " -sqrt(-2*(251*sqrt(3765)/9216 + 2159/1024)**(1/3) - 227/(96*(251*sqrt(3765)/9216 + 2159/1024)**(1/3)) + 1631/(32*sqrt(227/(96*(251*sqrt(3765)/9216 + 2159/1024)**(1/3)) + 2*(251*sqrt(3765)/9216 + 2159/1024)**(1/3) + 145/16)) + 145/8)/2 + 11/8 + sqrt(227/(96*(251*sqrt(3765)/9216 + 2159/1024)**(1/3)) + 2*(251*sqrt(3765)/9216 + 2159/1024)**(1/3) + 145/16)/2]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b2 = soln2[1][b]\n", "r2 = sp.solve(soln1[0][r].subs(b, b2) - r, r)\n", "r2" ] }, { "cell_type": "markdown", "id": "efade4ca-3dcf-4216-b169-216cc90dc34e", "metadata": {}, "source": [ "The four solutions can be plot together for comparison:\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "c209f5ba-c266-4410-9d90-27ac5af24e98", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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