From 33c3301dc2bfba0766b31a7d5959980ba71fd82b Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Tue, 18 Apr 2017 09:29:25 -0400 Subject: [PATCH] added lecture 23 --- lecture_01/octave-workspace | Bin 0 -> 153 bytes lecture_02/octave-workspace | Bin 0 -> 153 bytes lecture_20/octave-workspace | Bin 11 -> 153 bytes lecture_21/octave-workspace | Bin 5105 -> 4869 bytes lecture_22/octave-workspace | Bin 0 -> 1145 bytes .../lecture_23-checkpoint.ipynb | 6 + lecture_23/coriolis.m | 63 ++ lecture_23/eulode.m | 29 + lecture_23/lecture_23.ipynb | 610 ++++++++++++++++++ lecture_23/north_coriolis.m | 53 ++ lecture_23/octave-workspace | Bin 0 -> 15770 bytes lecture_23/predprey.m | 6 + lecture_23/rk4sys.m | 53 ++ 13 files changed, 820 insertions(+) create mode 100644 lecture_01/octave-workspace create mode 100644 lecture_02/octave-workspace create mode 100644 lecture_22/octave-workspace create mode 100644 lecture_23/.ipynb_checkpoints/lecture_23-checkpoint.ipynb create mode 100644 lecture_23/coriolis.m create mode 100644 lecture_23/eulode.m create mode 100644 lecture_23/lecture_23.ipynb create mode 100644 lecture_23/north_coriolis.m create mode 100644 lecture_23/octave-workspace create mode 100644 lecture_23/predprey.m create mode 100644 lecture_23/rk4sys.m diff --git a/lecture_01/octave-workspace b/lecture_01/octave-workspace new file mode 100644 index 0000000000000000000000000000000000000000..8c437bb6e55a5d1b6115661b3a20e86870909d32 GIT binary patch literal 153 zcmeZIE=ep))iu=hVPIxpU`Wg>29gX6|5<=Ua%xV_zyJULGXmL6K+FfkHXuRW)ST4Z s)VvZqpa4)UCy*#Ej4v)J%FIiLX#g3JmQ#{Vk|uVbru4khf}H#k0D5999{>OV literal 0 HcmV?d00001 diff --git a/lecture_02/octave-workspace b/lecture_02/octave-workspace new file mode 100644 index 0000000000000000000000000000000000000000..8c437bb6e55a5d1b6115661b3a20e86870909d32 GIT binary patch literal 153 zcmeZIE=ep))iu=hVPIxpU`Wg>29gX6|5<=Ua%xV_zyJULGXmL6K+FfkHXuRW)ST4Z s)VvZqpa4)UCy*#Ej4v)J%FIiLX#g3JmQ#{Vk|uVbru4khf}H#k0D5999{>OV literal 0 HcmV?d00001 diff --git a/lecture_20/octave-workspace b/lecture_20/octave-workspace index 41ef164d111fcfa9cc9ec079bd8194241d90356e..8c437bb6e55a5d1b6115661b3a20e86870909d32 100644 GIT binary patch literal 153 zcmeZIE=ep))iu=hVPIxpU`Wg>29gX6|5<=Ua%xV_zyJULGXmL6K+FfkHXuRW)ST4Z s)VvZqpa4)UCy*#Ej4v)J%FIiLX#g3JmQ#{Vk|uVbru4khf}H#k0D5999{>OV literal 11 ScmeZIE=ep))iu=hVE_OY#sfM4 diff --git a/lecture_21/octave-workspace b/lecture_21/octave-workspace index 398435fefbd4b6a70ccfb784b9a9ebd0fd888079..f2ecb23eff3ad2f689bdd44498246d85ded9c5e1 100644 GIT binary patch literal 4869 zcmeHJ`8$>S7T;zKG{~VzC?z+cQjuD3qSB<0Bg2*PNdq!nrOqLg$`O(#m5!d$r9&DB zr?pR^geW0HBGWePDUzbxy?x*Jocr8v_ql(7AKty*@3hwXeAZ{Z-)-p@;1cAaYoNP{ zCBb5`wul}UYgktF{#yOZpS);Ne3bUbVrf~#&#{P~K@q!vYPi3z{{B8gdTc^v zi-+~A>3MT%#3{>yk`}!LIlFj|jQ=C)Z-Ur-GCZDl$DB%<`E!QYCXMYK&p8dF67Bl`PNp3HiA}Mopf5LGzOOxFk7tQE{&O#A$MDq3`Qd<#V#^nX3Ig z(|(X;uSX>V^#mDqfTuyA)?^v>6$Q%&Ip#vM@H7hl( z+b~-1e9N+pEx5dNLf@t}%~6CK6sChwub6Z!n(l2zLpu;7E7|ns>+~bpSh3 z7oh6|sibaTL+S`aq^>~M8MczT!w}H{MeBm1bwV8^x}mlZ9Z|HdC|YM!DbXF3Oms-m zx}<2GQffrE)O(_1iq%FDUWX=zz1kOMuJw+9+DwMq4OePVg)~ zo{ZR5y?G@U3o25cPH*bMhR3%Ja)&$7NL9Y2es&jjxpw?x=bBF3rRO8S#~jr4Gq&;d z=|IOx1^#OKEqGGK;Cy0AGuC|AenD|_GkPX@B&v4TV@&*Kp;y>zj1byz+ykqyR^w~a z1jA}fGHX)kRjWkT=#sr#l*%w>ne5|%>IZneEMvC)t{a&3aK@8C*=v7VW}ex{oMZej zewjE-TqX}DFD6eWZw3d0i^0j@W_VzDVR&MA<8qcLO8W9~u=rC=Qz{?Z&#cT#-zdPt zTGOSJ_X}{?u`RfSCBUE@joj8c9_Bh`-ZKpm;KKNGb0+(V=G&yg6Dzs+(c$v+xyZ#0 zZniovLU?HZsW7WBorj0A4&JDp-;IV+%AXu1da$6UT(^ zhZU!fof*@CN7Z(3wJU2y#_7kpzApKN<5oF-EjN05@RA#<^-%M#wFTzev5WKL9e+>;v#QlqSY;_-_!Jxv1e}a z_)gte%zqG6qpkNF$nKsT73lE{rkEPWuErwRYFT7GS5O98`U#6wENVc>NG<7{Yz;^b zWvA-3)`78b$E6MXo51MR%3RKk7RYq(ycks60;xlRSHo|%L+;&yW!G1C!2MXBx=lF; 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This + % function takes the latitude (L) in degrees and mass (m) and calculates the trajectory + % of a particle with a 100 N load directed North. The initial conditions are set as L + % (in radians) * radius of Earth, 0 m/s initial x-velocity, 0 m E-W position (add to + % -72.261319 degrees for longitude of Storrs), 0 m/s initial E-W velocity, 10 m initial + % altitude, 0 m/s initial z-velocity [L*pi/180*R 0 0 0 10 0], the force is given as 100 + % N North, 0 West and 9.81*m z (neutrally buoyant) [100 0 9.81*m] + % + % the output of myode is ddr=[dx/dt d2x/dt2 dy/dt d2y/dt2 dz/dt d2z/dt2]' and the input + % to myode is r=[x dx/dt y dy/dt z dz/dt]' + % using ode23 solver solves for r as a function of time, here we solve from 0 to 200 s + % r(:,1) = x (the north-south position from 0 to 200 s) + % r(:,3) = x (the West-East position from 0 to 200 s) + % r(:,5) = x (the altitude from 0 to 200 s) + + % define ordinary differential equation in terms of 6 first order ODE's + function ddr = myode(t,r,R,L) + g=9.81; % acceleration due to gravity m/s^2 + l=10; % 10 m long cable + we=2*pi/23.934/3600; % rotation of Earth (each day is 23.934 hours long) + ddr=zeros(4,1); % initialize ddr + + ddr(1) = r(2); % x North(+) South (-) + ddr(2) = 2*we*r(4).*sin(L)-g/l*r(1); % dx/dt + ddr(3) = r(4); % y West (+) East (-) + ddr(4) = -2*we*(r(2).*sin(L))-g/l*r(3); % dy/dt + end + + R=6378.1e3; % radius of Earth in m + L=L*pi/180; + [t,r]=ode45(@(t,r) myode(t,r,R,L),[0 30000], [1 0 0 0 ]); + figure() + z=-sqrt(10^2-r(:,1).^2-r(:,3).^2); + figure(1) + we=2*pi/23.934/3600; % rotation of Earth (each day is 23.934 hours long) + + plot(t,tan(we*sin(L)*t),t,-r(:,3)./r(:,1),'.') + xlabel('time (s)','Fontsize',18) + ylabel('-y/x','Fontsize',18) + % Plot Coriolis effect path + figure(2) + title('Path at 0 hr, 4.1 hrs, 8.3 hrs','Fontsize',24) + N=length(t); + i1=[1:100]; i2=[floor(N/2):floor(N/2)+100]; i3=[N-100:N]; + plot3(r(i1,1),r(i1,3),z(i1)) + hold on + plot3(r(i2,1),r(i2,3),z(i2),'k-') + plot3(r(i3,1),r(i3,3),z(i3),'g-') + xlabel('X (m)','Fontsize',18) + ylabel('Y (m)','Fontsize',18) + zlabel('Z (m)','Fontsize',18) + title('Coriolis acceleration Foucalt Pendulum') + +% figure() +% % Plot Eotvos effect for deviation upwards +% plot(1e-3*(r(:,1)-r(1,1)),r(:,5)) +% xlabel('North (+km)','Fontsize',18) +% ylabel('Altitude (+m)','Fontsize',18) +% title('Eotvos effect with north force') +% +end + diff --git a/lecture_23/eulode.m b/lecture_23/eulode.m new file mode 100644 index 0000000..ceed97b --- /dev/null +++ b/lecture_23/eulode.m @@ -0,0 +1,29 @@ +function [t,y] = eulode(dydt,tspan,y0,h,varargin) +% eulode: Euler ODE solver +% [t,y] = eulode(dydt,tspan,y0,h,p1,p2,...): +% uses Euler's method to integrate an ODE +% input: +% dydt = name of the M-file that evaluates the ODE +% tspan = [ti, tf] where ti and tf = initial and +% final values of independent variable +% y0 = initial value of dependent variable +% h = step size +% p1,p2,... = additional parameters used by dydt +% output: +% t = vector of independent variable +% y = vector of solution for dependent variable +if nargin<4,error('at least 4 input arguments required'),end +ti = tspan(1);tf = tspan(2); +if ~(tf>ti),error('upper limit must be greater than lower'),end +t = (ti:h:tf)'; n = length(t); +% if necessary, add an additional value of t +% so that range goes from t = ti to tf +if t(n)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "a=1.2;b=0.6;c=0.8;d=0.3;\n", + "[t y] = eulode(@predprey,tspan,y0,h,a,b,c,d);\n", + "\n", + "plot(t,y(:,1),t,y(:,2),'--')\n", + "legend('prey','predator');\n", + "title('(a) Euler time plot')" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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N+8idYB7xgMJ4h2CoHeIdAMCigCCdBenzAfOIKyDeAQBsDAjSGagzEGAecQjE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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(y(:,1),y(:,2))\n", + "title('(b) Euler phase plane plot')" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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S+uxBo4ulxaS1Xrf8kKkGxYPJ3vrhHAMUEkKmboTXbVIck+xhb72a0bSf1w1S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\nQCEBAAAAUgAKCQAAAJACUEgAAACAFPx/zW4IgobeuzoAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "[t y] = rk4sys(@predprey,tspan,y0,h,a,b,c,d);\n", + "plot(t,y(:,1),t,y(:,2),'--')\n", + "title('(c) RK4 time plot')" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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F08fJGbhgl5kzZ27dunXHjh1VVVVHjhzhzTJOCKmvrx87dmxdXZ1du33zzTd5bxqkampq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\n4sSJjIyMFStW0M3efPPN/v37q1pSAAB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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(y(:,1),y(:,2))\n", + "title('(d) RK4 phase plane plot')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Systems of ODE's:\n", + "## The Coriolis Effect\n", + "\n", + "System of ODE's defined as:\n", + "```matlab\n", + " function ddr = coriolis_ode(t,r,R,L)\n", + " g=9.81; % acceleration due to gravity m/s^2\n", + " l=10; % 10 m long cable\n", + " we=2*pi/23.934/3600; % rotation of Earth (each day is 23.934 hours long)\n", + " ddr=zeros(4,1); % initialize ddr\n", + "\n", + " ddr(1) = r(2); % x North(+) South (-)\n", + " ddr(2) = 2*we*r(4).*sin(L)-g/l*r(1); % dx/dt \n", + " ddr(3) = r(4); % y West (+) East (-)\n", + " ddr(4) = -2*we*(r(2).*sin(L))-g/l*r(3); % dy/dt\n", + " end\n", + "```\n", + "\n", + "First, we will solve for the path of a neutrally-buoyant object with a 100-N force pointing North. It's path starts at 41.8084$^o$ lattitude (Storrs, CT)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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SpEkTJ07805/+dODAgQ8++KCmpoYtVlhYSERdu3ZVWt3Dw4OIKioq9Bs1ADQL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\nUj9+MzkgjNLJQEZY/bq6urCwsLS0tJEjR27durX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3UUIW6CkO9BQz8+PhPRcA0Pl4z/YNxo1pXjqYWYb+eADQmfjdIQ0dOpQ+slMD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\nuGtqarp69WpLS4uZmdmgQYPkbowUFRUVFRcX29r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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans =\n", + "\n", + " 0\n", + " 0.0000\n", + " 0.0000\n", + " 0.0000\n", + " 0.0000\n", + " 0.0000\n", + " 0.0000\n", + " 0.0000\n", + " 0.0000\n", + " 0.0000\n", + " 0.0000\n", + " 0.0000\n", + " 0.0001\n", + " 0.0001\n", + " 0.0002\n", + " 0.0003\n", + " 0.0003\n", + " 0.0006\n", + " 0.0009\n", + " 0.0013\n", + " 0.0016\n", + " 0.0031\n", + " 0.0047\n", + " 0.0063\n", + " 0.0078\n", + " 0.0157\n", + " 0.0235\n", + " 0.0314\n", + " 0.0392\n", + " 0.0785\n", + " 0.1177\n", + " 0.1570\n", + " 0.1962\n", + " 0.3925\n", + " 0.5887\n", + " 0.7850\n", + " 0.9812\n", + " 1.9624\n", + " 2.9436\n", + " 3.9248\n", + " 4.9060\n", + " 9.0087\n", + " 13.1115\n", + " 17.2142\n", + " 21.3169\n", + " 26.3169\n", + " 31.3169\n", + " 36.3169\n", + " 41.3169\n", + " 46.3169\n", + " 51.3169\n", + " 56.3169\n", + " 61.3169\n", + " 66.3169\n", + " 71.3169\n", + " 76.3169\n", + " 81.3169\n", + " 86.3169\n", + " 91.3169\n", + " 96.3169\n", + " 101.3169\n", + " 106.3169\n", + " 111.3169\n", + " 116.3169\n", + " 121.3169\n", + " 126.3169\n", + " 131.3169\n", + " 136.3169\n", + " 141.3169\n", + " 146.3169\n", + " 151.3169\n", + " 156.3169\n", + " 161.3169\n", + " 166.3169\n", + " 171.3169\n", + " 176.3169\n", + " 181.3169\n", + " 185.9877\n", + " 190.6584\n", + " 195.3292\n", + " 200.0000\n" + ] + } + ], + "source": [ + "north_coriolis(41.8084,1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "coriolis(41.8084)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Adaptive Runge-Kutta Methods\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ODE23 Solve non-stiff differential equations, low order method.\n", + " [TOUT,YOUT] = ODE23(ODEFUN,TSPAN,Y0) with TSPAN = [T0 TFINAL] integrates \n", + " the system of differential equations y' = f(t,y) from time T0 to TFINAL \n", + " with initial conditions Y0. ODEFUN is a function handle. For a scalar T\n", + " and a vector Y, ODEFUN(T,Y) must return a column vector corresponding \n", + " to f(t,y). Each row in the solution array YOUT corresponds to a time \n", + " returned in the column vector TOUT. To obtain solutions at specific \n", + " times T0,T1,...,TFINAL (all increasing or all decreasing), use TSPAN = \n", + " [T0 T1 ... TFINAL]. \n", + " \n", + " [TOUT,YOUT] = ODE23(ODEFUN,TSPAN,Y0,OPTIONS) solves as above with default\n", + " integration properties replaced by values in OPTIONS, an argument created \n", + " with the ODESET function. See ODESET for details. Commonly used options\n", + " are scalar relative error tolerance 'RelTol' (1e-3 by default) and vector\n", + " of absolute error tolerances 'AbsTol' (all components 1e-6 by default).\n", + " If certain components of the solution must be non-negative, use\n", + " ODESET to set the 'NonNegative' property to the indices of these\n", + " components.\n", + " \n", + " ODE23 can solve problems M(t,y)*y' = f(t,y) with mass matrix M that is\n", + " nonsingular. Use ODESET to set the 'Mass' property to a function handle \n", + " MASS if MASS(T,Y) returns the value of the mass matrix. If the mass matrix \n", + " is constant, the matrix can be used as the value of the 'Mass' option. If\n", + " the mass matrix does not depend on the state variable Y and the function\n", + " MASS is to be called with one input argument T, set 'MStateDependence' to\n", + " 'none'. ODE15S and ODE23T can solve problems with singular mass matrices. \n", + " \n", + " [TOUT,YOUT,TE,YE,IE] = ODE23(ODEFUN,TSPAN,Y0,OPTIONS) with the 'Events'\n", + " property in OPTIONS set to a function handle EVENTS, solves as above \n", + " while also finding where functions of (T,Y), called event functions, \n", + " are zero. For each function you specify whether the integration is \n", + " to terminate at a zero and whether the direction of the zero crossing \n", + " matters. These are the three column vectors returned by EVENTS: \n", + " [VALUE,ISTERMINAL,DIRECTION] = EVENTS(T,Y). For the I-th event function: \n", + " VALUE(I) is the value of the function, ISTERMINAL(I)=1 if the integration \n", + " is to terminate at a zero of this event function and 0 otherwise. \n", + " DIRECTION(I)=0 if all zeros are to be computed (the default), +1 if only \n", + " zeros where the event function is increasing, and -1 if only zeros where \n", + " the event function is decreasing. Output TE is a column vector of times \n", + " at which events occur. Rows of YE are the corresponding solutions, and \n", + " indices in vector IE specify which event occurred. \n", + " \n", + " SOL = ODE23(ODEFUN,[T0 TFINAL],Y0...) returns a structure that can be\n", + " used with DEVAL to evaluate the solution or its first derivative at \n", + " any point between T0 and TFINAL. The steps chosen by ODE23 are returned \n", + " in a row vector SOL.x. For each I, the column SOL.y(:,I) contains \n", + " the solution at SOL.x(I). If events were detected, SOL.xe is a row vector \n", + " of points at which events occurred. Columns of SOL.ye are the corresponding \n", + " solutions, and indices in vector SOL.ie specify which event occurred. \n", + " \n", + " Example \n", + " [t,y]=ode23(@vdp1,[0 20],[2 0]); \n", + " plot(t,y(:,1));\n", + " solves the system y' = vdp1(t,y), using the default relative error\n", + " tolerance 1e-3 and the default absolute tolerance of 1e-6 for each\n", + " component, and plots the first component of the solution. \n", + " \n", + " Class support for inputs TSPAN, Y0, and the result of ODEFUN(T,Y):\n", + " float: double, single\n", + " \n", + " See also ODE45, ODE113, ODE15S, ODE23S, ODE23T, ODE23TB, ODE15I,\n", + " ODESET, ODEPLOT, ODEPHAS2, ODEPHAS3, ODEPRINT, DEVAL,\n", + " ODEEXAMPLES, RIGIDODE, BALLODE, ORBITODE, FUNCTION_HANDLE.\n", + "\n", + " Reference page in Doc Center\n", + " doc ode23\n" + ] + } + ], + "source": [ + "help ode23" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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m+UZi0lXvghoSAAC4BAQkqCWzD0nmYQDmyOkcwoTf3gkBCaS0bOXsEoAX4E74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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "a=4;b=0.05;c=5;d=0.1;\n", + "tspan=[0,5];\n", + "[t23 y23] = ode23(@predprey,tspan,y0,h,a,b,c,d);\n", + "[t45,y45] = ode45(@predprey,tspan,y0,h,a,b,c,d);\n", + "plot(t23,y23(:,1),t23,y23(:,2),t45,y45(:,1),'--'...\n", + ",t45,y45(:,2),'--')\n", + "title('ode23- vs ode45--')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Matlab", + "language": "matlab", + "name": "matlab" + }, + "language_info": { + "codemirror_mode": "octave", + "file_extension": ".m", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "matlab", + "version": "0.11.0" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_23/north_coriolis.m b/lecture_23/north_coriolis.m new file mode 100644 index 0000000..28a2337 --- /dev/null +++ b/lecture_23/north_coriolis.m @@ -0,0 +1,53 @@ +function [t,r] = coriolis(L,m) + % In class we ran this function using L=41.8084 (the latitude of Storrs, CT). This + % function takes the latitude (L) in degrees and mass (m) and calculates the trajectory + % of a particle with a 100 N load directed North. The initial conditions are set as L + % (in radians) * radius of Earth, 0 m/s initial x-velocity, 0 m E-W position (add to + % -72.261319 degrees for longitude of Storrs), 0 m/s initial E-W velocity, 10 m initial + % altitude, 0 m/s initial z-velocity [L*pi/180*R 0 0 0 10 0], the force is given as 100 + % N North, 0 West and 9.81*m z (neutrally buoyant) [100 0 9.81*m] + % + % the output of myode is ddr=[dx/dt d2x/dt2 dy/dt d2y/dt2 dz/dt d2z/dt2]' and the input + % to myode is r=[x dx/dt y dy/dt z dz/dt]' + % using ode23 solver solves for r as a function of time, here we solve from 0 to 200 s + % r(:,1) = x (the north-south position from 0 to 200 s) + % r(:,3) = x (the West-East position from 0 to 200 s) + % r(:,5) = x (the altitude from 0 to 200 s) + + % define ordinary differential equation in terms of 6 first order ODE's + function ddr = myode(t,r,F,m,R) + Fx=F(1); Fy=F(2); Fz=F(3); % set each Force component + g=9.81; % acceleration due to gravity m/s^2 + we=2*pi/23.934/3600; % rotation of Earth (each day is 23.934 hours long) + ddr=zeros(6,1); % initialize ddr + + ddr(1) = r(2); % x North(+) South (-) + ddr(2) = 2*we*r(2).*sin(r(1)/R)-r(6).*cos(r(1)/R)+Fx/m; % dx/dt + ddr(3) = r(4); % y West (+) East (-) + ddr(4) = -2*we*(r(2).*sin(r(1)/R)-r(6).*cos(r(1)/R))+Fy/m; % dy/dt + ddr(5) = r(6); % z altitude + ddr(6) = -2*we*r(4).*cos(r(1)/R)+Fz/m-g; % dz/dt + end + + R=6378.1e3; % radius of Earth in m + % Applied force is 100 N in Northern direction and z-direction equals force of gravity + % (neutrally buoyant travel) + F= [ 100 0 9.81*m]; %Applied force in N + [t,r]=ode45(@(t,r) myode(t,r,[100 0 9.81*m],m, R),[0 200], [L*pi/180*R 0 0 0 10 0]); + figure() + % Plot Coriolis effect for deviation Westward + plot(r(:,3),1e-3*(r(:,1)-r(1,1))) + xlabel('West (+m)','Fontsize',18) + ylabel('North (+km)','Fontsize',18) + text(0,0, 'Storrs, CT') + title('Coriolis acceleration with north force') + + figure() + % Plot Eotvos effect for deviation upwards + plot(1e-3*(r(:,1)-r(1,1)),r(:,5)) + xlabel('North (+km)','Fontsize',18) + ylabel('Altitude (+m)','Fontsize',18) + title('Eotvos effect with north force') + +end + diff --git a/lecture_23/octave-workspace b/lecture_23/octave-workspace new file mode 100644 index 0000000000000000000000000000000000000000..31e53e3a72e847321998fa34938cd3dd0d2ef869 GIT binary patch literal 15770 zcmZwO30#cd_c-up+H0o0DMAuiq7`#KV` zv=9-|h_b}&)4u$l&*yvo%kTC5&+C=9JEz-yhPiXjz4vKy@Y1={RWL7@@dS#(=_d;32fwb(EHe_{;N8w+3k z^RU8y0t^3r?!SNHH~1$S{9nvk0a-%6B|nfAq=c*@zmqlOPx3eUhm?|XQb8(76{#jQWF1*g zHjs^E6WL6*kga4J*-kR}@9P$l42RkzqeX3!(WW-Z=un$vbg4};dekNveQJ}80kuiS zklG|;L~WAcQk!IW)Fv5YYLko!wMoX5+9YH4pEi<0QcN=D6eoqGm}D#{P6|me$yidH z6p~_+v7$IBB*i4dr#LAj#Ux`*aZ*T%Nydiaq>vPoOb3dSLQ+gJ9Vt!?lqONioTEr8p@h#Ux|@pSV4Vq<|EXB2r9B zNTwV0Cy^A8LQ+JENeRg~P=69h0VyO!q?nYDOm}4ddDxRk3P>R-BE_VHWO`745=j9m zBt@i{l#q-g^(T=OkU~;Kib)B{^rZeIk^)jlibydjA(>v(pF~nX3P}+uCM6`BshEEr 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(Lotka-Volterra equations) + yp=zeros(2,1); + yp(1)=a*y(1)-b*y(1)*y(2); + yp(2)=-c*y(2)+d*y(1)*y(2); +end diff --git a/lecture_23/rk4sys.m b/lecture_23/rk4sys.m new file mode 100644 index 0000000..fe747cb --- /dev/null +++ b/lecture_23/rk4sys.m @@ -0,0 +1,53 @@ +function [tp,yp] = rk4sys(dydt,tspan,y0,h,varargin) +% rk4sys: fourth-order Runge-Kutta for a system of ODEs +% [t,y] = rk4sys(dydt,tspan,y0,h,p1,p2,...): integrates +% a system of ODEs with fourth-order RK method +% input: +% dydt = name of the M-file that evaluates the ODEs +% tspan = [ti, tf]; initial and final times with output +% generated at interval of h, or +% = [t0 t1 ... tf]; specific times where solution output +% y0 = initial values of dependent variables +% h = step size +% p1,p2,... = additional parameters used by dydt +% output: +% tp = vector of independent variable +% yp = vector of solution for dependent variables +if nargin<4,error('at least 4 input arguments required'), end +if any(diff(tspan)<=0),error('tspan not ascending order'), end +n = length(tspan); +ti = tspan(1);tf = tspan(n); +if n == 2 + t = (ti:h:tf)'; n = length(t); + if t(n)h,hh = h;end + while(1) + if tt+hh>tend,hh = tend-tt;end + k1 = dydt(tt,y(i,:),varargin{:})'; + ymid = y(i,:) + k1.*hh./2; + k2 = dydt(tt+hh/2,ymid,varargin{:})'; + ymid = y(i,:) + k2*hh/2; + k3 = dydt(tt+hh/2,ymid,varargin{:})'; + yend = y(i,:) + k3*hh; + k4 = dydt(tt+hh,yend,varargin{:})'; + phi = (k1+2*(k2+k3)+k4)/6; + y(i+1,:) = y(i,:) + phi*hh; + tt = tt+hh; + i=i+1; + if tt>=tend,break,end + end + np = np+1; tp(np) = tt; yp(np,:) = y(i,:); + if tt>=tf,break,end +end \ No newline at end of file