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computational mechanics | ||
the dog had 4 legs and weighed 10.0 lbs | ||
are you awake?computational mechanics | ||
the dog had 4 legs and weighed 10.0 lbs | ||
are you awake? |
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## When using the command prompt, anything in your path or working directory can be run either as a script, function or class (to define objects) | ||
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Questions from last class: | ||
- I downloaded GitHub to my desktop but I cannot sign into my UConn account like I can online. | ||
- I checked my grades on HuskyCt recently and I received a 0 / 100 for Homework 1. | ||
- It is very hard to tell if what I'm doing on github is right or wrong. | ||
- How often will be using our laptops during the lecture? | ||
- How many frogs would it take to move a car that is stuck in the snow? And what would be the approximate cost to do so | ||
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$m_{frog}$=22.7 g (https://en.wikipedia.org/wiki/Common_frog) | ||
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$v_{frog}$=17 kph = 4.72 m/s (http://purelyfacts.com/question/14/is-a-toad-faster-than-a-frog?DDA=113&DDB=40) | ||
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$m_{car}$=1000 kg (reasonable guess) | ||
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conservation of momentum: | ||
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$mv_{1} +mv_{2} = mv_{1}'+mv_{2}' = m_{total}v_{2}'$ | ||
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```matlab | ||
number_of_frogs = 1; | ||
v2=0; | ||
while v2 < 1 % 1 m/s | ||
m_frogs=number_of_frogs*22.7e-3; | ||
number_of_frogs=number_of_frogs+1; | ||
p1=(m_frogs)*4.72; % momentum 1 | ||
v2=p1/(m_frogs+1000); % p2=p1, so v2=p1/m_total | ||
end | ||
number_of_frogs | ||
``` | ||
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number_of_frogs = | ||
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11844 | ||
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```matlab | ||
%myscript | ||
``` | ||
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```matlab | ||
%plot --format svg | ||
``` | ||
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When using the GUI, your command history is saved, but it is better to save your work either as a script or a function or combination of both | ||
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Creating a default graph script: `setdefaults.m` | ||
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```matlab | ||
set(0, 'defaultAxesFontSize', 16) | ||
set(0,'defaultTextFontSize',14) | ||
set(0,'defaultLineLineWidth',3) | ||
``` | ||
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```matlab | ||
set(0, 'defaultAxesFontSize', 16) | ||
set(0,'defaultTextFontSize',14) | ||
set(0,'defaultLineLineWidth',3) | ||
``` | ||
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```matlab | ||
t_linear=linspace(0,10,100); | ||
plot(t_linear,t_linear.^2) | ||
xlabel('time (s)') | ||
ylabel('displacement (m)') | ||
``` | ||
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 | ||
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#EOL | ||
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## Graphics can be produced with a number of functions | ||
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2-D plots, 3-D plots, contour plots, 3D contour plots ... | ||
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```matlab | ||
x=linspace(-1,1,21); y=linspace(-1,1,21); | ||
[X,Y]=meshgrid(x,y); | ||
Z=(X.*Y.^3-X.^3.*Y) | ||
``` | ||
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Z = | ||
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Columns 1 through 7 | ||
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0 0.1710 0.2880 0.3570 0.3840 0.3750 0.3360 | ||
-0.1710 0 0.1224 0.2016 0.2430 0.2520 0.2340 | ||
-0.2880 -0.1224 0 0.0840 0.1344 0.1560 0.1536 | ||
-0.3570 -0.2016 -0.0840 0 0.0546 0.0840 0.0924 | ||
-0.3840 -0.2430 -0.1344 -0.0546 0 0.0330 0.0480 | ||
-0.3750 -0.2520 -0.1560 -0.0840 -0.0330 0 0.0180 | ||
-0.3360 -0.2340 -0.1536 -0.0924 -0.0480 -0.0180 0 | ||
-0.2730 -0.1944 -0.1320 -0.0840 -0.0486 -0.0240 -0.0084 | ||
-0.1920 -0.1386 -0.0960 -0.0630 -0.0384 -0.0210 -0.0096 | ||
-0.0990 -0.0720 -0.0504 -0.0336 -0.0210 -0.0120 -0.0060 | ||
0 0 0 0 0 0 0 | ||
0.0990 0.0720 0.0504 0.0336 0.0210 0.0120 0.0060 | ||
0.1920 0.1386 0.0960 0.0630 0.0384 0.0210 0.0096 | ||
0.2730 0.1944 0.1320 0.0840 0.0486 0.0240 0.0084 | ||
0.3360 0.2340 0.1536 0.0924 0.0480 0.0180 0.0000 | ||
0.3750 0.2520 0.1560 0.0840 0.0330 0 -0.0180 | ||
0.3840 0.2430 0.1344 0.0546 -0.0000 -0.0330 -0.0480 | ||
0.3570 0.2016 0.0840 0 -0.0546 -0.0840 -0.0924 | ||
0.2880 0.1224 0 -0.0840 -0.1344 -0.1560 -0.1536 | ||
0.1710 0.0000 -0.1224 -0.2016 -0.2430 -0.2520 -0.2340 | ||
0 -0.1710 -0.2880 -0.3570 -0.3840 -0.3750 -0.3360 | ||
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Columns 8 through 14 | ||
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0.2730 0.1920 0.0990 0 -0.0990 -0.1920 -0.2730 | ||
0.1944 0.1386 0.0720 0 -0.0720 -0.1386 -0.1944 | ||
0.1320 0.0960 0.0504 0 -0.0504 -0.0960 -0.1320 | ||
0.0840 0.0630 0.0336 0 -0.0336 -0.0630 -0.0840 | ||
0.0486 0.0384 0.0210 0 -0.0210 -0.0384 -0.0486 | ||
0.0240 0.0210 0.0120 0 -0.0120 -0.0210 -0.0240 | ||
0.0084 0.0096 0.0060 0 -0.0060 -0.0096 -0.0084 | ||
0 0.0030 0.0024 0 -0.0024 -0.0030 0 | ||
-0.0030 0 0.0006 0 -0.0006 0 0.0030 | ||
-0.0024 -0.0006 0 0 0.0000 0.0006 0.0024 | ||
0 0 0 0 0 0 0 | ||
0.0024 0.0006 -0.0000 0 0 -0.0006 -0.0024 | ||
0.0030 0 -0.0006 0 0.0006 0 -0.0030 | ||
0 -0.0030 -0.0024 0 0.0024 0.0030 0 | ||
-0.0084 -0.0096 -0.0060 0 0.0060 0.0096 0.0084 | ||
-0.0240 -0.0210 -0.0120 0 0.0120 0.0210 0.0240 | ||
-0.0486 -0.0384 -0.0210 0 0.0210 0.0384 0.0486 | ||
-0.0840 -0.0630 -0.0336 0 0.0336 0.0630 0.0840 | ||
-0.1320 -0.0960 -0.0504 0 0.0504 0.0960 0.1320 | ||
-0.1944 -0.1386 -0.0720 0 0.0720 0.1386 0.1944 | ||
-0.2730 -0.1920 -0.0990 0 0.0990 0.1920 0.2730 | ||
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Columns 15 through 21 | ||
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-0.3360 -0.3750 -0.3840 -0.3570 -0.2880 -0.1710 0 | ||
-0.2340 -0.2520 -0.2430 -0.2016 -0.1224 -0.0000 0.1710 | ||
-0.1536 -0.1560 -0.1344 -0.0840 0 0.1224 0.2880 | ||
-0.0924 -0.0840 -0.0546 0 0.0840 0.2016 0.3570 | ||
-0.0480 -0.0330 0.0000 0.0546 0.1344 0.2430 0.3840 | ||
-0.0180 0 0.0330 0.0840 0.1560 0.2520 0.3750 | ||
-0.0000 0.0180 0.0480 0.0924 0.1536 0.2340 0.3360 | ||
0.0084 0.0240 0.0486 0.0840 0.1320 0.1944 0.2730 | ||
0.0096 0.0210 0.0384 0.0630 0.0960 0.1386 0.1920 | ||
0.0060 0.0120 0.0210 0.0336 0.0504 0.0720 0.0990 | ||
0 0 0 0 0 0 0 | ||
-0.0060 -0.0120 -0.0210 -0.0336 -0.0504 -0.0720 -0.0990 | ||
-0.0096 -0.0210 -0.0384 -0.0630 -0.0960 -0.1386 -0.1920 | ||
-0.0084 -0.0240 -0.0486 -0.0840 -0.1320 -0.1944 -0.2730 | ||
0 -0.0180 -0.0480 -0.0924 -0.1536 -0.2340 -0.3360 | ||
0.0180 0 -0.0330 -0.0840 -0.1560 -0.2520 -0.3750 | ||
0.0480 0.0330 0 -0.0546 -0.1344 -0.2430 -0.3840 | ||
0.0924 0.0840 0.0546 0 -0.0840 -0.2016 -0.3570 | ||
0.1536 0.1560 0.1344 0.0840 0 -0.1224 -0.2880 | ||
0.2340 0.2520 0.2430 0.2016 0.1224 0 -0.1710 | ||
0.3360 0.3750 0.3840 0.3570 0.2880 0.1710 0 | ||
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```matlab | ||
contour(X,Y,Z) | ||
``` | ||
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 | ||
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```matlab | ||
mesh(X,Y,Z) | ||
``` | ||
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 | ||
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```matlab | ||
pcolor(X,Y,Z) | ||
``` | ||
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 | ||
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## Functions | ||
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So far, everything has been executed as a script, or calling a built-in function. Now we begin building our own functions. | ||
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Functions are saved in memory (or better yet) in a folder in your path or current directory | ||
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Example of storing function in memory | ||
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$f(x,y) = (xy^{3}-x^{3}y)$ | ||
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```matlab | ||
f= @(x,y) (x.*y.^3-x.^3.*y) | ||
``` | ||
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f = | ||
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@(x,y)(x.*y.^3-x.^3.*y) | ||
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```matlab | ||
f(0.1,-0.5) | ||
``` | ||
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ans = | ||
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-0.0120 | ||
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Here we will save a function called `my_function` as `my_function.m` | ||
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```matlab | ||
function [vx,vy] = my_function(x,y,t) | ||
% Help documentation of "my_function" | ||
% This function computes the velocity in the x- and y-directions given | ||
% three vectors of position in x- and y-directions as a function of time | ||
% x = x-position | ||
% y = y-position | ||
% t = time | ||
% output | ||
% vx = velocity in x-direction | ||
% vy = velocity in y-direction | ||
vx=zeros(length(t),1); | ||
vy=zeros(length(t),1); | ||
vx(1:end-1) = diff(x)./diff(t); % calculate vx as delta x/delta t | ||
vy(1:end-1) = diff(y)./diff(t); % calculate vy as delta y/delta t | ||
vx(end) = vx(end-1); | ||
vy(end) = vy(end-1); | ||
end | ||
``` | ||
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```matlab | ||
help my_function | ||
``` | ||
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Help documentation of "my_function" | ||
This function computes the velocity in the x- and y-directions given | ||
three vectors of position in x- and y-directions as a function of time | ||
x = x-position | ||
y = y-position | ||
t = time | ||
output | ||
vx = velocity in x-direction | ||
vy = velocity in y-direction | ||
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```matlab | ||
t=linspace(0,10,100)'; | ||
x=t.^3; % vx = 3*t^2 | ||
y=t.^2/2; % vy = t | ||
[vx,vy]=my_function(x,y,t); | ||
``` | ||
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```matlab | ||
yyaxis left | ||
plot(t(1:10:end),vx(1:10:end),'o',t,3*t.^2) | ||
ylabel('v_{x}') | ||
yyaxis right | ||
plot(t(1:10:end),vy(1:10:end),'s',t, t) | ||
ylabel('v_{y}') | ||
xlabel('time') | ||
``` | ||
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 | ||
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Now, create a new function that calls 'my_function' called, `my_caller.m` | ||
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```matlab | ||
help my_caller | ||
``` | ||
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Help documentation of "my_caller" | ||
This function computes the acceleration in the x- and y-directions given | ||
three vectors of position in x- and y-directions as a function of time | ||
x = x-position | ||
y = y-position | ||
t = time | ||
output | ||
ax = velocity in x-direction | ||
ay = velocity in y-direction | ||
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```matlab | ||
[ax,ay]=my_caller(x,y,t); | ||
``` | ||
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```matlab | ||
yyaxis left | ||
plot(t(1:10:end),ax(1:10:end),'o',t,6*t) | ||
ylabel('a_{x}') | ||
yyaxis right | ||
plot(t(1:10:end),ay(1:10:end),'s',t, 1*t./t) | ||
ylabel('a_{x}') | ||
xlabel('time') | ||
axis([0,10,0,3]) | ||
``` | ||
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 | ||
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```matlab | ||
diff_match_dims(x,t) | ||
``` | ||
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[0;31mUndefined function 'diff_match_dims' for input arguments of type 'double'. | ||
[0m | ||
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```matlab | ||
``` |
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f=100; | ||
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for i=1:10 | ||
g=i^2; | ||
if f==g | ||
fprintf('we made it\n') | ||
else | ||
fprintf('not yet\n') | ||
end | ||
end | ||
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