Difference between revisions of "Matlab Basics"

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Now we can define the time that the projectile reaches its maximum height, and then determine what the maximum height is.  We use the variables we just defined:
 
Now we can define the time that the projectile reaches its maximum height, and then determine what the maximum height is.  We use the variables we just defined:
 
<source lang="matlab">
 
<source lang="matlab">
−
   t  = (vt-v0)/a;            % time when the bullet stops (maximum height)
+
   t  = (vt-v0)/a;            % time (s) when the bullet stops (maximum height)
−
   yt = y0 + v0*t + a*t^2/2;  % maximum height.
+
   yt = y0 + v0*t + a*t^2/2;  % maximum height (feet).
 
</source>
 
</source>
 
If we omit the <tt>;</tt> on the line for <tt>yt</tt> MATLAB will print its value.  Or we can simply type the variable and MATLAB will print it.  Doing this we see that the projectile reaches a height of 1,397.5 feet at 9.317 seconds (neglecting air resistance).  This illustrates the convenience of using variables.  The MATLAB code reads much like our original equations did.
 
If we omit the <tt>;</tt> on the line for <tt>yt</tt> MATLAB will print its value.  Or we can simply type the variable and MATLAB will print it.  Doing this we see that the projectile reaches a height of 1,397.5 feet at 9.317 seconds (neglecting air resistance).  This illustrates the convenience of using variables.  The MATLAB code reads much like our original equations did.

Revision as of 10:18, 19 August 2008

The Command Window

MATLAB's command window can be used as a very powerful calculator. The >> indicates that MATLAB is ready to accept a command. It works much like your calculator. For example, 

 >> 1 + cos(pi/2)
 ans = 
      1
 >> 5^2   % square 5
 ans =
      25

Note that anything following a % on a line is ignored. This allows us to include comments in our calculations.

Defining Variables

By using variables instead of numbers, our calculations look much like they would on paper. For example, from physics we know that projectile motion (in the absence of air resistance) is governed by the equations

\begin{align} y(t) &= y(0) + v(0) \, t + \tfrac{1}{2} a \, t^2, \\ v(t) &= v(0) + a\,t, \end{align}

where y(0) and v(0) are the position and velocity of the projectile at time t=0 and a is the acceleration.

Assume that we have the following problem: 

 A bullet is shot upward with an initial velocity of 300 feet per second (fps).  Determine the maximum height of the bullet.

The maximum height occurs when v(t)=0. We can solve the equation for v(t) to find

t=\frac{v(t)-v(0)}{a}.

This gives the time at which the bullet reaches its maximum height. We can then use the equation for y(t) to determine how high it is at that time.

Let's solve this in MATLAB. First we define the initial height, the initial velocity, and the acceleration. We also know the final velocity - it is zero. 

  y0 = 0.0;    % initial height (feet)
  v0 = 300;    % initial velocity (feet/s)
  vt = 0.0;    % final velocity (feet/s)
  a  = -32.2;  % gravitational acceleration (feet^2/s)

Now we can define the time that the projectile reaches its maximum height, and then determine what the maximum height is. We use the variables we just defined: 

  t  = (vt-v0)/a;            % time (s) when the bullet stops (maximum height)
  yt = y0 + v0*t + a*t^2/2;  % maximum height (feet).

If we omit the ; on the line for yt MATLAB will print its value. Or we can simply type the variable and MATLAB will print it. Doing this we see that the projectile reaches a height of 1,397.5 feet at 9.317 seconds (neglecting air resistance). This illustrates the convenience of using variables. The MATLAB code reads much like our original equations did.

Useful Commands

Often we want to see what variables we have defined in the MATLAB workspace. Or we may want to clear a variable. The commands in the following table illustrate several useful tools for managing variables.

Command Description Example (try these out)
who Lists variables currently defined in MATLAB. 
a = 5; b = 6; c = linspace(0,50,10);
who
whos Similar to who, but gives additional information. 
a = 5; b = 6; c = linspace(0,50,10);
whos
clear Clear all variables defined. 
a = 5; b = 6; c = linspace(0,50,10);
clear;            % clears all variables
who;              % displays nothing - no variables defined.
a=2; b=5; c=a+b;
clear a b;        % only clears a and b.  c is still here.
who;              % tells us that c is defined.
clc Clears the MATLAB workspace. Doesn't clear variables 
clc
save saves variables to a file that can be loaded later. 
clear;
a=5; b=6; c=a+b*2;
save myVariables;  % saves all variables to the file "myVariables.mat"
save bcVars b c;   % saves b and c only to "bcVars.mat"
load loads variables from a file 
clear;
a=5; b=6; c=a+b*2;
save myVariables;
save bcVars b c;
clear;
load bcVars;       % b and c are now defined.
who;
clear;
load myVariables;  % a b and c are all defined.
who;
help provides help on how to use a command 
help clear;
help load;
help save;

Basic Operations

MATLAB supports basic operations

Basic Operators
Operator Description Examples
+ Addition 
1 + 2            % displays 3
b = 1+2;         % assigns 3 to the variable b.
a = cos(pi)+2.0; % a=1
- Subtraction 
1 - 2               % displays -1
b = 1-2;            % assigns -1 to the variable b.
a = sqrt(-4*b)+2.0; % a=4
* Multiplication 
2.2*3.3       % displays 6.6
a = 2.2*3.3;  % assigns 6.6 to a.
b = (pi/4);   % assigns sqrt(2)/2 to b.
/ Division 
6.6/2.2       % dispays 3.3
a = 6.6/2.2;  % assigns 3.3 to a.
b = sqrt(a/pi)*exp(a);
^ Power 
2^3                 % displays 8
a = 2^3 + 243^0.2;  % assigns 11 to a.
( ) Parentheses 
a = (2+5)*3;  % assigns 21 to a
b = 2+5*3;    % assigns 17 to b
c = 2*(a-10); % assigns 22 to c

NOTE: if you are using arrays, then the / and * operators have different behavior! See the page on array arithmetic for more information.


In addition, MATLAB has many built-in functions. Type help elfun at the MATLAB command prompt for a list. Some commonly used functions are given here:

Function Description
cos The cosine function
sin The sine function
tan The tangent function
sqrt The square-root, \sqrt(x)=x^{1/2}
exp The exponential function
log10 The base-10 log function, \log(10^x)=x
log The natural log function, \ln(\exp(x))=x
abs The absolute value, \left|x\right|


M-Files

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An M-file is a series of MATLAB commands that you save in a file. Then you can re-run them easily and make changes without re-entering everything again. Anything that can be done in the command window can also be done from an m-file.

MATLAB's Path

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