ENG004 ALGORITHMS & INT. TO PROGRAMMING
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ENG004 ALGORITHMS & INT. TO PROGRAMMING
Week 4
“Arrays and Matrix Operations III”
Ahmet Anıl Dindar
21.03.2007
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ENG004.01 2
The class facts
E-mail address: [email protected]
Class web page: http://web.iku.edu.tr/courses/insaat/eng004/
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Last week
First Program! Arrays (Matrices) The user input command : “input” The arrays in formulas Trigonometric calculations Examples:
“Gauss Number summation”
“Fligth Problem”
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This week
More programming... Accessing elements of arrays and matrices Element by element matrix operations Example
“Fligth Problem”
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Fligth Problem
We want to calculate the followings?
1- The duration of the object’s fligth.(Tflight)
2- The highest altitude of the fligth. (ymax)
3- The distance between the origin and landing point. (xmax)
PS: 2 weeks later, we will visulize our findings!
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Fligth ProblemThe formulation of the flight problem is:
20
0
21)()(
)()(
tgtSinVty
tCosVtx
By using this equation we determine the following equations
1- The duration of the object’s fligth.(tflight)
2- The highest altitude of the fligth. (ymax)
3- The distance between the origin and landing point. (xmax)
g
SinVt fligth
)(2 0
20max )2(21)2()( flightflight tgtSinVy
)()(0max flighttCosVx
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Let’s re-write the Fligth Problem codeThe user should enter the initial values into the computer
1- The initial velocity (V0)2- The horizontal angle ()3- The gravity acceleration (g)
Then the code should calculate 1- The duration of the object’s fligth.(Tflight)2- The highest altitude of the fligth. (ymax)3- The distance between the origin and landing point. (xmax)
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The Code of the Flight Problem
clc,clear,close all
v0=input('Please enter the initial velocity : ')alfa=input('Pleae enter the horizontal angle : ')g=input('Please enter the gravity acceleration : ')
The user input lines
The computer calculations
% The following line calculates the duration of the fligthtflight=2*v0*sin(alfa*pi/180)/g ;
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The Code of the Flight Problem
% xmax xmax=v0*cos(alfa*pi/180)*tfligth;% ymaxymax=v0*sin(alfa*pi/180)*tf/2-.5*g*(tf/2)^2;
The computer should calculate the xmax and ymax.
The “;” does not allow the program to display the results in the command window.If you want to see the results, you need new commands : “fpritnf”
% let's see the results in the command windowfprintf('The highest altitude of the flight is %.2f m \n',ymax)fprintf('The distance of the landing point is %.2f m \n',xmax)
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The Code of the Flight ProblemLet’s estimate the max values from the x and y series.In order to create the x and y series, we need to create the time series:
% time seriest=(0:.1:tf);
We use the formulations for the x and y series
% now let's calculate the x and y seriesx=v0*cos(alfa*pi/180)*t;y=v0*sin(alfa*pi/180)*t-.5*g*(t).^2;
20
0
21)()(
)()(
tgtSinVty
tCosVtx
Think of the “.”
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The Code of the Flight ProblemLet’s estimate the max values from the x and y series.In order to create the x and y series, we need to create the time series:
% min and max commandsxmax2=max(x);ymax2=max(y);
% let's see the results in the command windowfprintf('The highest altitude of the flight is %.2f m \n',ymax2)fprintf('The distance of the landing point is %.2f m \n',xmax2)
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The Code of the Flight ProblemLet’s run the program and see the results!
clc,clear,close allv0=input('Please enter the initial velocity : ')alfa=input('Pleae enter the horizontal angle : ')g=input('Please enter the gravitaty acceleration : ')% The following line calculates the duration of the fligthtf=2*v0*sin(alfa*pi/180)/g;% max distancexmax=v0*cos(alfa*pi/180)*tf;% ymaxymax=v0*sin(alfa*pi/180)*tf/2-.5*g*(tf/2)^2;% let's see the results in the command windowfprintf('The highest altitude of the flight is %.2f m \n',ymax)fprintf('The distance of the landing point is %.2f m \n',xmax)% time seriest=(0:.1:tf);% now let's calculate the x and y seriesx=v0*cos(alfa*pi/180)*t;y=v0*sin(alfa*pi/180)*t-.5*g*(t).^2;% min and max commandsxmax2=max(x);ymax2=max(y);fprintf('The highest altitude of the flight is %.2f m (by using alternative way)\n',ymax2)fprintf('The distance of the landing point is %.2f m (by using alternative way)\n',xmax2)
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Assignment 3Let’s create a vector matrix (x) and perform the following formulation.
f(x)=variable1*x^3+variable2*x^2-2*x
And estimate the min and max values.
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Send your diary files to class e-mail
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Next week...
Weeks Date Class Assignment
1 21.02 Introduction to the class Registration
2 28.02 Exploring MATLAB Assignment 1
3 07.03 Arrays and Matrix Operations N.A.
4 14.03 Arrays and Matrix Operations Assignment 2
5 21.03 Arrays and Matrix Operations Assignment 3
6 28.03 Polynomials and curve-fitting Assignment 4
7 04.04 Descriptive statistics Assignment 5
8 11.04 Programming Elements of MATLAB N.A.
9 18.04 Programming Elements of MATLAB Assignment 6
10 25.04 Programming Elements of MATLAB Assignment 7
11 02.05 Plotting and Animations N.A.
12 09.05 Plotting and Animations Assignment 8
13 16.05 Numerical Integration Assignment 9
14 23.05 Symbolic Math Assignment 10
15 30.05 Take-home final project N.A.
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See you next week!