I want to know how to get plots like in the image in MATLAB. I have the following code. With the angular velocity data, how do I get a figure like show in the image I = [0.3; 0.2; 0.4];w_per1 = [0.1; 0.001; 0.001];w_per2 = [0.001; 0.1; 0.001];w_per3 = [0.001; 0.001; 0.1];L = [0;0;0];t = 0:300;sigma = [0.3; 0.3; 0.3];% Finidng EP from MRPEP = MRPtoEP(sigma)% Using ode45 to integrate KDEoptions = odeset('RelTol',1e-10,'AbsTol',1e-10);[t, y] = ode45(@dwdt_KDE_EP, t, [EP; w_per2], options);% Extract the Euler parameters and angular velocitiesw_p1 = y(:, 5:7)'; function dqwdt = dwdt_KDE_EP(~,EPw) I = [0.3; 0.2; 0.4]; L = [0;0;0]; EP = EPw(1:4); w = EPw(5:7); dqdt = zeros(4,1); dwdt = zeros(3,1); dqdt(1) = 0.5*(EP(4)*w(1) - EP(3)*w(2) + EP(2)*w(3)); dqdt(2) = 0.5*(EP(3)*w(1) + EP(4)*w(2) - EP(1)*w(3)); dqdt(3) = 0.5*(-EP(2)*w(1) + EP(1)*w(2) + EP(4)*w(3)); dqdt(4) = -0.5*(EP(1)*w(1) + EP(2)*w(2) + EP(3)*w(3)); dwdt(1) = (-(I(3) - I(2))*w(2)*w(3) + L(1)) / I(1); dwdt(2) = (-(I(1) - I(3))*w(3)*w(1) + L(2)) / I(2); dwdt(3) = (-(I(2) - I(1))*w(1)*w(2) + L(3)) / I(3); % Combine the time derivatives into a single vector dqwdt = [dqdt; dwdt]; endfunction [EP] = MRPtoEP(sigma) EP1 = (2*sigma(1)) / (1 + dot(sigma, sigma)); EP2 = (2*sigma(2)) / (1 + dot(sigma, sigma)); EP3 = (2*sigma(3)) / (1 + dot(sigma, sigma)); EP4 = (1 - dot(sigma, sigma)) / (1 + dot(sigma, sigma)); EP = [EP1; EP2; EP3; EP4];end ### Description of the DiagramsThe image contains two 3D plots, each depicting vector fields in three-dimensional space. Both plots show elliptical paths, vectors, and axes, which are presumably related to rotational dynamics or another physical system.#### Left Plot- **Axes:** - The x-axis is labeled as \( \hat{n}_1 \), ranging approximately from -0.12 to -0.04. - The y-axis is labeled as \( \hat{n}_2 \), ranging from -0.16 to -0.08. - The z-axis is labeled as \( \hat{n}_3 \), ranging from -0.14 to -0.11. - **Elements:** - There is a single elliptical trajectory in black. - A black vector labeled \( \vec{\omega} \) is tangent to the ellipse path. - \( \vec{\omega}_0 \) is marked by an arrowhead along the trajectory. - A blue vector labeled \( \vec{H} \), with an arrowhead, is directed outward from the plane of the ellipse. A dotted blue line represents its path or alignment, possibly indicating an angular momentum vector.#### Right Plot- **Axes:** - The x-axis is labeled as \( \hat{n}_1 \), ranging approximately from 0.05 to 0.2. - The y-axis is labeled as \( \hat{n}_2 \), ranging from -0.1 to 0.2. - The z-axis is labeled as \( \hat{n}_3 \), ranging from -0.3 to -0.15.- **Elements:** - There are multiple concentric elliptical paths in black. - A black vector labeled \( \vec{\omega} \) is tangent to the outer ellipse. - The arrowhead represents the vector \( \vec{\omega}_0 \). - A blue vector labeled \( \vec{H} \), along with a dotted blue path line, is displayed, similar to the left plot.### Legend- **\( \vec{\omega} \):** Represents the angular velocity vector in both plots.- **\( \vec{\omega}_0 \):** Denotes a specific point or direction along the trajectory.- **\( \vec{H} \):** Represents another vector, potentially the angular momentum, shown

Answered: Image /qna-images/answer/5c97eb10-2fd8-4fdf-ae81-5efa01e4d238.jpg

I want to know how to get plots like in the image in MATLAB. I have the following code. With the angular velocity data, how do I get a figure like show in the image I = [0.3; 0.2; 0.4]; w_per1 = [0.1; 0.001; 0.001]; w_per2 = [0.001; 0.1; 0.001]; w_per3 = [0.001; 0.001; 0.1]; L = [0;0;0]; t = 0:300; sigma = [0.3; 0.3; 0.3]; % Finidng EP from MRP EP = MRPtoEP(sigma) % Using ode45 to integrate KDE options = odeset('RelTol',1e-10,'AbsTol',1e-10); [t, y] = ode45(@dwdt_KDE_EP, t, [EP; w_per2], options); % Extract the Euler parameters and angular velocities w_p1 = y(:, 5:7)'; function dqwdt = dwdt_KDE_EP(~,EPw) I = [0.3; 0.2; 0.4]; L = [0;0;0]; EP = EPw(1:4); w = EPw(5:7); dqdt = zeros(4,1); dwdt = zeros(3,1); dqdt(1) = 0.5(EP(4)w(1) - EP(3)w(2) + EP(2)w(3)); dqdt(2) = 0.5(EP(3)w(1) + EP(4)w(2) - EP(1)w(3)); dqdt(3) = 0.5(-EP(2)w(1) + EP(1)w(2) + EP(4)w(3)); dqdt(4) = -0.5(EP(1)w(1) + EP(2)w(2) + EP(3)w(3)); dwdt(1) = (-(I(3) - I(2))w(2)w(3) + L(1)) / I(1); dwdt(2) = (-(I(1) - I(3))w(3)w(1) + L(2)) / I(2); dwdt(3) = (-(I(2) - I(1))w(1)w(2) + L(3)) / I(3); % Combine the time derivatives into a single vector dqwdt = [dqdt; dwdt]; end function [EP] = MRPtoEP(sigma) EP1 = (2sigma(1)) / (1 + dot(sigma, sigma)); EP2 = (2sigma(2)) / (1 + dot(sigma, sigma)); EP3 = (2*sigma(3)) / (1 + dot(sigma, sigma)); EP4 = (1 - dot(sigma, sigma)) / (1 + dot(sigma, sigma)); EP = [EP1; EP2; EP3; EP4]; end

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

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I want to know how to get plots like in the image in MATLAB. I have the following code. With the angular velocity data, how do I get a figure like show in the image

I = [0.3; 0.2; 0.4];
w_per1 = [0.1; 0.001; 0.001];
w_per2 = [0.001; 0.1; 0.001];
w_per3 = [0.001; 0.001; 0.1];
L = [0;0;0];
t = 0:300;
sigma = [0.3; 0.3; 0.3];

% Finidng EP from MRP
EP = MRPtoEP(sigma)

% Using ode45 to integrate KDE
options = odeset('RelTol',1e-10,'AbsTol',1e-10);
[t, y] = ode45(@dwdt_KDE_EP, t, [EP; w_per2], options);

% Extract the Euler parameters and angular velocities
w_p1 = y(:, 5:7)';

function dqwdt = dwdt_KDE_EP(~,EPw)

I = [0.3; 0.2; 0.4];
L = [0;0;0];

EP = EPw(1:4);
w = EPw(5:7);

dqdt = zeros(4,1);
dwdt = zeros(3,1);

dqdt(1) = 0.5*(EP(4)*w(1) - EP(3)*w(2) + EP(2)*w(3));
dqdt(2) = 0.5*(EP(3)*w(1) + EP(4)*w(2) - EP(1)*w(3));
dqdt(3) = 0.5*(-EP(2)*w(1) + EP(1)*w(2) + EP(4)*w(3));
dqdt(4) = -0.5*(EP(1)*w(1) + EP(2)*w(2) + EP(3)*w(3));

dwdt(1) = (-(I(3) - I(2))*w(2)*w(3) + L(1)) / I(1);
dwdt(2) = (-(I(1) - I(3))*w(3)*w(1) + L(2)) / I(2);
dwdt(3) = (-(I(2) - I(1))*w(1)*w(2) + L(3)) / I(3);

% Combine the time derivatives into a single vector
dqwdt = [dqdt; dwdt];

end

function [EP] = MRPtoEP(sigma)

EP1 = (2*sigma(1)) / (1 + dot(sigma, sigma));
EP2 = (2*sigma(2)) / (1 + dot(sigma, sigma));
EP3 = (2*sigma(3)) / (1 + dot(sigma, sigma));
EP4 = (1 - dot(sigma, sigma)) / (1 + dot(sigma, sigma));

EP = [EP1; EP2; EP3; EP4];

end

### Description of the Diagrams

The image contains two 3D plots, each depicting vector fields in three-dimensional space. Both plots show elliptical paths, vectors, and axes, which are presumably related to rotational dynamics or another physical system.

#### Left Plot

- **Axes:**
- The x-axis is labeled as \( \hat{n}_1 \), ranging approximately from -0.12 to -0.04.
- The y-axis is labeled as \( \hat{n}_2 \), ranging from -0.16 to -0.08.
- The z-axis is labeled as \( \hat{n}_3 \), ranging from -0.14 to -0.11.

- **Elements:**
- There is a single elliptical trajectory in black.
- A black vector labeled \( \vec{\omega} \) is tangent to the ellipse path.
- \( \vec{\omega}_0 \) is marked by an arrowhead along the trajectory.
- A blue vector labeled \( \vec{H} \), with an arrowhead, is directed outward from the plane of the ellipse. A dotted blue line represents its path or alignment, possibly indicating an angular momentum vector.

#### Right Plot

- **Axes:**
- The x-axis is labeled as \( \hat{n}_1 \), ranging approximately from 0.05 to 0.2.
- The y-axis is labeled as \( \hat{n}_2 \), ranging from -0.1 to 0.2.
- The z-axis is labeled as \( \hat{n}_3 \), ranging from -0.3 to -0.15.

- **Elements:**
- There are multiple concentric elliptical paths in black.
- A black vector labeled \( \vec{\omega} \) is tangent to the outer ellipse.
- The arrowhead represents the vector \( \vec{\omega}_0 \).
- A blue vector labeled \( \vec{H} \), along with a dotted blue path line, is displayed, similar to the left plot.

### Legend
- **\( \vec{\omega} \):** Represents the angular velocity vector in both plots.
- **\( \vec{\omega}_0 \):** Denotes a specific point or direction along the trajectory.
- **\( \vec{H} \):** Represents another vector, potentially the angular momentum, shown

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