Answered: Figure 1 File Edit View Insert Tools…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Question

For the following MATLAB code, I need to answer a few questions. Can you identify the curves as elliptic functions? Which curves reflect the sn, cn, and dn functions?
From the curves, determine the maximum amplitudes and the period corresponding to
each angular velocity component.

clc;

clear all;

I = [500; 125; 425];

w = [0.2; 0.1; 0.2];

rev = 0:0.01:10;

C = eye(3);

% Using ode45 to integrate the KDE and DDE

options = odeset('RelTol',1e-9,'AbsTol',1e-9);

result = ode45(@K_DDE, rev, [w; I; C(:)], options);

v = result.x;

% Extracting information from the ode45 solver

w = result.y(1:3, :);

C_ode = reshape(result.y(7:end, :), [3,3,length(v)]);

plot(v, w)

xlabel('rev')

ylabel('w (rad/s)')

legend('w1', 'w2', 'w3')

% Functions

function dwCdt = K_DDE(~, w_IC)

% Extracting the initial condtions to a variable

w = w_IC(1:3);

I = w_IC(4:6);

C = reshape(w_IC(7:end), [3, 3]);

I1 = I(1);

I2 = I(2);

I3 = I(3);

K1 = -(I3-I2)/I1;

K2 = -(I1-I3)/I2;

K3 = -(I2-I1)/I3;

% Kinematic Differential Equations

dCdt = zeros(9,1);

dCdt(1) = 2*pi*(C(1,2)*w(3) - C(1,3)*w(2));

dCdt(2) = 2*pi*(C(1,3)*w(1) - C(1,1)*w(3));

dCdt(3) = 2*pi*(C(1,1)*w(2) - C(1,2)*w(1));

dCdt(4) = 2*pi*(C(2,2)*w(3) - C(2,3)*w(2));

dCdt(5) = 2*pi*(C(2,3)*w(1) - C(2,1)*w(3));

dCdt(6) = 2*pi*(C(2,1)*w(2) - C(2,2)*w(1));

dCdt(7) = 2*pi*(C(3,2)*w(3) - C(3,3)*w(2));

dCdt(8) = 2*pi*(C(3,3)*w(1) - C(3,1)*w(3));

dCdt(9) = 2*pi*(C(3,1)*w(2) - C(3,2)*w(1));

% Dynamical Differential Equations

dwdt = zeros(3,1);

dwdt(1) = 2*pi*K1*w(2)*w(3);

dwdt(2) = 2*pi*K2*w(1)*w(3);

dwdt(3) = 2*pi*K3*w(1)*w(2);

% Combining the w and C into one output matrix

dwCdt = [dwdt; 0; 0; 0; dCdt(:)];

end

function dwCdt2 = K_DDE2(~, w_en)

% Extracting the initial condtions to a variable

w = w_en(1:3);

C = reshape(w_en(4:12), [3, 3]);

Z = w_en(13);

I = 0.060214;

J = 0.015707;

x = (J/I) - 1;

y = Z - 1;

s = Z;

% Kinematic Differential Equations

dCdt = zeros(9,1);

dCdt(1) = 2*pi*(C(1,2)*(w(3)-C(2,3)) - C(1,3)*(w(2)-C(2,2)-s));

dCdt(2) = 2*pi*(C(1,3)*(w(1)-C(2,1)) - C(1,1)*(w(3)-C(2,3)));

dCdt(3) = 2*pi*(C(1,1)*(w(2)-C(2,2)-s) - C(1,2)*(w(1)-C(2,1)));

dCdt(4) = 2*pi*(C(2,2)*(w(3)-C(2,3)) - C(2,3)*(w(2)-C(2,2)-s));

dCdt(5) = 2*pi*(C(2,3)*(w(1)-C(2,1)) - C(2,1)*(w(3)-C(2,3)));

dCdt(6) = 2*pi*(C(2,1)*(w(2)-C(2,2)-s) - C(2,2)*(w(1)-C(2,1)));

dCdt(7) = 2*pi*(C(3,2)*(w(3)-C(2,3)) - C(3,3)*(w(2)-C(2,2)-s));

dCdt(8) = 2*pi*(C(3,3)*(w(1)-C(2,1)) - C(3,1)*(w(3)-C(2,3)));

dCdt(9) = 2*pi*(C(3,1)*(w(2)-C(2,2)-s) - C(3,2)*(w(1)-C(2,1)));

% Dynamical Differential Equations

dwdt = zeros(3,1);

dwdt(1) = 2*pi*(6*(-x)*(C(3,2))*(C(3,3)) - ...

(-x)*w(2)*w(3) + s*w(3));

dwdt(2) = 0;

dwdt(3) = 2*pi*(-12*(-x)*(C(3,1))*(C(3,2))+...

(-x)*w(1)*w(2) + s*w(1));

% Combining the w and C into one output matrix

dwCdt2 = [dwdt; dCdt(:); 0];

end

Figure 1
File Edit View Insert Tools Desktop Window Help
0.3
w (rad/s)
0.2
0.1
-0.1
-0.2
-0.3
0
1
2
3
4
5
rev
9
-
☐
W1
w2
w3
Х
7
8
9
10

Expert Solution

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Control Systems Engineering

Mechanical Engineering

ISBN:

9781118170519

Author:

Norman S. Nise

Publisher:

WILEY

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:

9781337093347

Author:

Barry J. Goodno, James M. Gere

Publisher:

Cengage Learning

Engineering Mechanics: Statics

Mechanical Engineering

ISBN:

9781118807330

Author:

James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher:

WILEY

SEE MORE TEXTBOOKS

Figure 1 File Edit View Insert Tools Desktop Window Help 0.3 w (rad/s) 0.2 0.1 -0.1 -0.2 -0.3 0 1 2 3 4 5 rev 9 - ☐ W1 w2 w3 Х 7 8 9 10