I am having trouble with the folloiwng MATLAB code. I am getting an error that says "unrecognized function or variable 'numericalPropogatorOptions". I have the aerospace toolbox and the aerospace blockset added. what add on do I have to download to use that function. How do I make this code work? % Define Keplerian Elements a = 29599.8; e = 0.0001; i = 0.9774; Omega = 1.3549; w = 0; M = 0.2645; [RECI, VECI] = Kepler2RV(a, e, i, Omega, w, M); initialState = [RECI * 1e3; VECI * 1e3]; % Initial position (m) and velocity (m/s) % Define constants mu = 3.986004418e14; % Gravitational constant (m^3/s^2) earthRadius = 6378.1363 * 1e3; % Earth radius in meters j2 = 1.08263e-3; % J2 perturbation coefficient % Define propagator options propOptions = numericalPropagatorOptions('CentralBody', 'Earth', ... 'GravitationalParameter', mu, ... 'InitialState', initialState, ... 'OutputTimeStep', 300); % Output every 300 seconds % Add perturbations addGravityModel(propOptions, 'Degree', 2, 'Order', 0); % J2 effect addDragModel(propOptions, 'AtmosphereModel', 'Exponential', ... 'ReferenceArea', 1.0, 'DragCoefficient', 2.2, ... 'Mass', 500); % Atmospheric drag addSolarRadiationPressureModel(propOptions, 'ReferenceArea', 1.0, ... 'Reflectivity', 1.3, 'Mass', 500); % SRP addThirdBodyGravity(propOptions, 'Moon'); % Third-body effect from the Moon addThirdBodyGravity(propOptions, 'Sun'); % Third-body effect from the Sun % Propagate the orbit endTime = 300 * 300; % 300 steps, each of 300 seconds [t, state] = numericalPropagator(endTime, propOptions); % Extract position and velocity for plotting position = state(:, 1:3); % Position in ECI (meters) velocity = state(:, 4:6); % Velocity in ECI (meters/second) % Plot the orbit plot3(position(:, 1), position(:, 2), position(:, 3)); xlabel('X (m)'); ylabel('Y (m)'); zlabel('Z (m)'); title('Simulated Orbit with Perturbations in ECI'); grid on; function [RECI, VECI] = Kepler2RV(a, e, i, Omega, w, M) mu = 398600.441799999971; % Earth's Standard Gravitational Parameter (GM) Eps = 2.22044604925031e-8; % Machine epsilon E = SolveKepler(M,e,Eps); % Eccentric Anomaly from Mean Anomaly M = 2*atan(sqrt((1+e)/(1-e))*tan(E/2)); % True Anomaly obtained from Eccentric Anomaly p = a*(1 - e^2); % Semiparameter (km) % Position Coordinates in Perifocal Coordinate System x = (p*cos(M)) / (1 + e*cos(M)); % x-coordinate (km) y = (p*sin(M)) / (1 + e*cos(M)); % y-coordinate (km) z = 0; % z-coordinate (km) vx = -(mu/p)^(1/2) * sin(M); % velocity in x (km/s) vy = (mu/p)^(1/2) * (e + cos(M)); % velocity in y (km/s) vz = 0; % velocity in z (km/s) % Transformation Matrix (3 Rotations) t_rot = [cos(Omega)*cos(w)-sin(Omega)*sin(w)*cos(i) ... (-1)*cos(Omega)*sin(w)-sin(Omega)*cos(w)*cos(i) ... sin(Omega)*sin(i); ... sin(Omega)*cos(w)+cos(Omega)*sin(w)*cos(i) ... (-1)*sin(Omega)*sin(w)+cos(Omega)*cos(w)*cos(i) ... (-1)*cos(Omega)*sin(i); ... sin(w)*sin(i) cos(w)*sin(i) cos(i)]; % Transformation Perifocal xyz to ECI RECI = t_rot*[x y z]'; VECI = t_rot*[vx vy vz]'; end function E = SolveKepler(M,e,Eps) % Iterative Solution of Kepler's equation (M = E-e*sin(E)) %========================================================================== % Inputs: M = Mean Anomaly (rad) % e = Eccentricity % Eps = Machine epsilon % Output: E = Eccentric Anomaly (rad) %========================================================================== E0 = M; E1 = E0 - (E0 - e*sin(E0) - M)/(1 -e*cos(E0)); while (abs(E1-E0) > Eps) E0 = E1; E1 = E0 - (E0 - e*sin(E0) - M)/(1 - e*cos(E0)); end E = E1; end

I am having trouble with the folloiwng MATLAB code. I am getting an error that says "unrecognized function or variable 'numericalPropogatorOptions". I have the aerospace toolbox and the aerospace blockset added. what add on do I have to download to use that function. How do I make this code work? % Define Keplerian Elements a = 29599.8; e = 0.0001; i = 0.9774; Omega = 1.3549; w = 0; M = 0.2645; [RECI, VECI] = Kepler2RV(a, e, i, Omega, w, M); initialState = [RECI * 1e3; VECI * 1e3]; % Initial position (m) and velocity (m/s) % Define constants mu = 3.986004418e14; % Gravitational constant (m^3/s^2) earthRadius = 6378.1363 * 1e3; % Earth radius in meters j2 = 1.08263e-3; % J2 perturbation coefficient % Define propagator options propOptions = numericalPropagatorOptions('CentralBody', 'Earth', ... 'GravitationalParameter', mu, ... 'InitialState', initialState, ... 'OutputTimeStep', 300); % Output every 300 seconds % Add perturbations addGravityModel(propOptions, 'Degree', 2, 'Order', 0); % J2 effect addDragModel(propOptions, 'AtmosphereModel', 'Exponential', ... 'ReferenceArea', 1.0, 'DragCoefficient', 2.2, ... 'Mass', 500); % Atmospheric drag addSolarRadiationPressureModel(propOptions, 'ReferenceArea', 1.0, ... 'Reflectivity', 1.3, 'Mass', 500); % SRP addThirdBodyGravity(propOptions, 'Moon'); % Third-body effect from the Moon addThirdBodyGravity(propOptions, 'Sun'); % Third-body effect from the Sun % Propagate the orbit endTime = 300 * 300; % 300 steps, each of 300 seconds [t, state] = numericalPropagator(endTime, propOptions); % Extract position and velocity for plotting position = state(:, 1:3); % Position in ECI (meters) velocity = state(:, 4:6); % Velocity in ECI (meters/second) % Plot the orbit plot3(position(:, 1), position(:, 2), position(:, 3)); xlabel('X (m)'); ylabel('Y (m)'); zlabel('Z (m)'); title('Simulated Orbit with Perturbations in ECI'); grid on; function [RECI, VECI] = Kepler2RV(a, e, i, Omega, w, M) mu = 398600.441799999971; % Earth's Standard Gravitational Parameter (GM) Eps = 2.22044604925031e-8; % Machine epsilon E = SolveKepler(M,e,Eps); % Eccentric Anomaly from Mean Anomaly M = 2atan(sqrt((1+e)/(1-e))tan(E/2)); % True Anomaly obtained from Eccentric Anomaly p = a(1 - e^2); % Semiparameter (km) % Position Coordinates in Perifocal Coordinate System x = (pcos(M)) / (1 + ecos(M)); % x-coordinate (km) y = (psin(M)) / (1 + ecos(M)); % y-coordinate (km) z = 0; % z-coordinate (km) vx = -(mu/p)^(1/2) sin(M); % velocity in x (km/s) vy = (mu/p)^(1/2) * (e + cos(M)); % velocity in y (km/s) vz = 0; % velocity in z (km/s) % Transformation Matrix (3 Rotations) t_rot = [cos(Omega)cos(w)-sin(Omega)sin(w)cos(i) ... (-1)cos(Omega)sin(w)-sin(Omega)cos(w)cos(i) ... sin(Omega)sin(i); ... sin(Omega)cos(w)+cos(Omega)sin(w)cos(i) ... (-1)sin(Omega)sin(w)+cos(Omega)cos(w)cos(i) ... (-1)cos(Omega)sin(i); ... sin(w)sin(i) cos(w)sin(i) cos(i)]; % Transformation Perifocal xyz to ECI RECI = t_rot[x y z]'; VECI = t_rot[vx vy vz]'; end function E = SolveKepler(M,e,Eps) % Iterative Solution of Kepler's equation (M = E-esin(E)) %========================================================================== % Inputs: M = Mean Anomaly (rad) % e = Eccentricity % Eps = Machine epsilon % Output: E = Eccentric Anomaly (rad) %========================================================================== E0 = M; E1 = E0 - (E0 - esin(E0) - M)/(1 -ecos(E0)); while (abs(E1-E0) > Eps) E0 = E1; E1 = E0 - (E0 - esin(E0) - M)/(1 - ecos(E0)); end E = E1; 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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Question

% Define Keplerian Elements

a = 29599.8; e = 0.0001; i = 0.9774; Omega = 1.3549; w = 0; M = 0.2645;

[RECI, VECI] = Kepler2RV(a, e, i, Omega, w, M);

initialState = [RECI * 1e3; VECI * 1e3]; % Initial position (m) and velocity (m/s)

% Define constants

mu = 3.986004418e14; % Gravitational constant (m^3/s^2)

earthRadius = 6378.1363 * 1e3; % Earth radius in meters

j2 = 1.08263e-3; % J2 perturbation coefficient

% Define propagator options

propOptions = numericalPropagatorOptions('CentralBody', 'Earth', ...

'GravitationalParameter', mu, ...

'InitialState', initialState, ...

'OutputTimeStep', 300); % Output every 300 seconds

% Add perturbations

addGravityModel(propOptions, 'Degree', 2, 'Order', 0); % J2 effect

addDragModel(propOptions, 'AtmosphereModel', 'Exponential', ...

'ReferenceArea', 1.0, 'DragCoefficient', 2.2, ...

'Mass', 500); % Atmospheric drag

addSolarRadiationPressureModel(propOptions, 'ReferenceArea', 1.0, ...

'Reflectivity', 1.3, 'Mass', 500); % SRP

addThirdBodyGravity(propOptions, 'Moon'); % Third-body effect from the Moon

addThirdBodyGravity(propOptions, 'Sun'); % Third-body effect from the Sun

% Propagate the orbit

endTime = 300 * 300; % 300 steps, each of 300 seconds

[t, state] = numericalPropagator(endTime, propOptions);

% Extract position and velocity for plotting

position = state(:, 1:3); % Position in ECI (meters)

velocity = state(:, 4:6); % Velocity in ECI (meters/second)

% Plot the orbit

plot3(position(:, 1), position(:, 2), position(:, 3));

xlabel('X (m)'); ylabel('Y (m)'); zlabel('Z (m)');

title('Simulated Orbit with Perturbations in ECI');

grid on;

function [RECI, VECI] = Kepler2RV(a, e, i, Omega, w, M)

mu = 398600.441799999971; % Earth's Standard Gravitational Parameter (GM)

Eps = 2.22044604925031e-8; % Machine epsilon

E = SolveKepler(M,e,Eps); % Eccentric Anomaly from Mean Anomaly

M = 2*atan(sqrt((1+e)/(1-e))*tan(E/2)); % True Anomaly obtained from Eccentric Anomaly

p = a*(1 - e^2); % Semiparameter (km)

% Position Coordinates in Perifocal Coordinate System

x = (p*cos(M)) / (1 + e*cos(M)); % x-coordinate (km)

y = (p*sin(M)) / (1 + e*cos(M)); % y-coordinate (km)

z = 0; % z-coordinate (km)

vx = -(mu/p)^(1/2) * sin(M); % velocity in x (km/s)

vy = (mu/p)^(1/2) * (e + cos(M)); % velocity in y (km/s)

vz = 0; % velocity in z (km/s)

% Transformation Matrix (3 Rotations)

t_rot = [cos(Omega)*cos(w)-sin(Omega)*sin(w)*cos(i) ...

(-1)*cos(Omega)*sin(w)-sin(Omega)*cos(w)*cos(i) ...

sin(Omega)*sin(i); ...

sin(Omega)*cos(w)+cos(Omega)*sin(w)*cos(i) ...

(-1)*sin(Omega)*sin(w)+cos(Omega)*cos(w)*cos(i) ...

(-1)*cos(Omega)*sin(i); ...

sin(w)*sin(i) cos(w)*sin(i) cos(i)];

% Transformation Perifocal xyz to ECI

RECI = t_rot*[x y z]';

VECI = t_rot*[vx vy vz]';

end

function E = SolveKepler(M,e,Eps)

% Iterative Solution of Kepler's equation (M = E-e*sin(E))

%==========================================================================

% Inputs: M = Mean Anomaly (rad)

% e = Eccentricity

% Eps = Machine epsilon

% Output: E = Eccentric Anomaly (rad)

%==========================================================================

E0 = M;

E1 = E0 - (E0 - e*sin(E0) - M)/(1 -e*cos(E0));

while (abs(E1-E0) > Eps)

E0 = E1;

E1 = E0 - (E0 - e*sin(E0) - M)/(1 - e*cos(E0));

end

E = E1;

end

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