is there a specific way where i can convert it with ease from latex to matlab
an example of an equation i want to know how can i write it in matlab form from latex
example 1:
begin{equation} h_{k}=frac {A(m+1)}{2 pi d_{k}^{2}}cos ^{m}(phi _{k})T(psi _{k})g(psi _{k})cos (psi _{k}), end{equation}

example 2:

begin{align} tilde {R}_{k rightarrow j}!=! begin{cases} !! frac {B}{2} log _{2}left ({1 + frac {left ({ h_{k} a_{j} }right )^{2}} {sum _{i=j+1}^{K}left ({ h_{k} a_{i} }right )^{2} + varepsilon sum _{i=1}^{j-1}left ({ h_{k} a_{i} }right )^{2}+ 1/rho } }right ) geq T_{j},\ qquad j leq k,j neq K;\ !! frac {B}{2}log _{2} left ({! 1!+!frac {left ({ h_{K} a_{j} }right )^{2}} {varepsilon sum _{i=1}^{j-1}left ({ h_{K} a_{i} }right )^{2}+1/rho }}right ) !geq ! T_{j} , quad j=k=K;end{cases}!!!!!!!notag \ {}end{align}is there a specific way where i can convert it with ease from latex to matlab
an example of an equation i want to know how can i write it in matlab form from latex
example 1:
begin{equation} h_{k}=frac {A(m+1)}{2 pi d_{k}^{2}}cos ^{m}(phi _{k})T(psi _{k})g(psi _{k})cos (psi _{k}), end{equation}

example 2:

begin{align} tilde {R}_{k rightarrow j}!=! begin{cases} !! frac {B}{2} log _{2}left ({1 + frac {left ({ h_{k} a_{j} }right )^{2}} {sum _{i=j+1}^{K}left ({ h_{k} a_{i} }right )^{2} + varepsilon sum _{i=1}^{j-1}left ({ h_{k} a_{i} }right )^{2}+ 1/rho } }right ) geq T_{j},\ qquad j leq k,j neq K;\ !! frac {B}{2}log _{2} left ({! 1!+!frac {left ({ h_{K} a_{j} }right )^{2}} {varepsilon sum _{i=1}^{j-1}left ({ h_{K} a_{i} }right )^{2}+1/rho }}right ) !geq ! T_{j} , quad j=k=K;end{cases}!!!!!!!notag \ {}end{align} is there a specific way where i can convert it with ease from latex to matlab
an example of an equation i want to know how can i write it in matlab form from latex
example 1:
begin{equation} h_{k}=frac {A(m+1)}{2 pi d_{k}^{2}}cos ^{m}(phi _{k})T(psi _{k})g(psi _{k})cos (psi _{k}), end{equation}

example 2:

begin{align} tilde {R}_{k rightarrow j}!=! begin{cases} !! frac {B}{2} log _{2}left ({1 + frac {left ({ h_{k} a_{j} }right )^{2}} {sum _{i=j+1}^{K}left ({ h_{k} a_{i} }right )^{2} + varepsilon sum _{i=1}^{j-1}left ({ h_{k} a_{i} }right )^{2}+ 1/rho } }right ) geq T_{j},\ qquad j leq k,j neq K;\ !! frac {B}{2}log _{2} left ({! 1!+!frac {left ({ h_{K} a_{j} }right )^{2}} {varepsilon sum _{i=1}^{j-1}left ({ h_{K} a_{i} }right )^{2}+1/rho }}right ) !geq ! T_{j} , quad j=k=K;end{cases}!!!!!!!notag \ {}end{align} how to, latex, tex, special characters MATLAB Answers — New Questions

​

Hello everyone,
I am trying to output a square matrix that is N x M in size, where N = M. In my case, N = 3. So this is a "3×3" matrix
I have a variable that’s called "Kernel". This variable is calculated as an equation in terms of "z" and "z_prime".
My values in z_prime will vary from L / 2N to (2N-1)*(L/2N) , in steps of "L/N".
My "z" variable will be used as an "integration variable" as seen below.

I am trying to calculate an output called the "Z Matrix" which will integrate the "Kernal" variable across specific ranges.
I attached a .pdf file to clarify my end goal.
See the .pdf file attached:
Z_Matrix_Output.pdf

My Integration Limits for "z" will be going from:
z_start = 0 : L/N : (N-1) * (L/N)
z_end = L/N : L/N : L

As of right now, I’m getting the error:
Operator ‘*’ is not supported for operands of type ‘function_handle’.
This is after I tried using "function handles" in my code.

In my attempt, I have tried to use for loops and created function handles to make it easier to generate this matrix.However, I didn’t end up with a "N X M" matrix, I just ended up with a "1 X N" matrix.
I know that there is a way to use "nested" for loops to generate a square matrix of an "N X M" size. However, I wasn’t quite sure on how to implement that in MATLAB for my case.

I have tried to look through different questions/answers on the Mathworks Forum regarding converting equations of two variables into "matrix elements". However, I wasn’t able to find anything that was relevant to my case.

I attached my MATLAB Code for reference.
See MATLAB .m file attached:
Z_Calculation.mHello everyone,
I am trying to output a square matrix that is N x M in size, where N = M. In my case, N = 3. So this is a "3×3" matrix
I have a variable that’s called "Kernel". This variable is calculated as an equation in terms of "z" and "z_prime".
My values in z_prime will vary from L / 2N to (2N-1)*(L/2N) , in steps of "L/N".
My "z" variable will be used as an "integration variable" as seen below.

I am trying to calculate an output called the "Z Matrix" which will integrate the "Kernal" variable across specific ranges.
I attached a .pdf file to clarify my end goal.
See the .pdf file attached:
Z_Matrix_Output.pdf

My Integration Limits for "z" will be going from:
z_start = 0 : L/N : (N-1) * (L/N)
z_end = L/N : L/N : L

As of right now, I’m getting the error:
Operator ‘*’ is not supported for operands of type ‘function_handle’.
This is after I tried using "function handles" in my code.

In my attempt, I have tried to use for loops and created function handles to make it easier to generate this matrix.However, I didn’t end up with a "N X M" matrix, I just ended up with a "1 X N" matrix.
I know that there is a way to use "nested" for loops to generate a square matrix of an "N X M" size. However, I wasn’t quite sure on how to implement that in MATLAB for my case.

I have tried to look through different questions/answers on the Mathworks Forum regarding converting equations of two variables into "matrix elements". However, I wasn’t able to find anything that was relevant to my case.

I attached my MATLAB Code for reference.
See MATLAB .m file attached:
Z_Calculation.m Hello everyone,
I am trying to output a square matrix that is N x M in size, where N = M. In my case, N = 3. So this is a "3×3" matrix
I have a variable that’s called "Kernel". This variable is calculated as an equation in terms of "z" and "z_prime".
My values in z_prime will vary from L / 2N to (2N-1)*(L/2N) , in steps of "L/N".
My "z" variable will be used as an "integration variable" as seen below.

I am trying to calculate an output called the "Z Matrix" which will integrate the "Kernal" variable across specific ranges.
I attached a .pdf file to clarify my end goal.
See the .pdf file attached:
Z_Matrix_Output.pdf

My Integration Limits for "z" will be going from:
z_start = 0 : L/N : (N-1) * (L/N)
z_end = L/N : L/N : L

As of right now, I’m getting the error:
Operator ‘*’ is not supported for operands of type ‘function_handle’.
This is after I tried using "function handles" in my code.

In my attempt, I have tried to use for loops and created function handles to make it easier to generate this matrix.However, I didn’t end up with a "N X M" matrix, I just ended up with a "1 X N" matrix.
I know that there is a way to use "nested" for loops to generate a square matrix of an "N X M" size. However, I wasn’t quite sure on how to implement that in MATLAB for my case.

I have tried to look through different questions/answers on the Mathworks Forum regarding converting equations of two variables into "matrix elements". However, I wasn’t able to find anything that was relevant to my case.

I attached my MATLAB Code for reference.
See MATLAB .m file attached:
Z_Calculation.m matrix array, matrix, matrix manipulation, integration, numerical integration MATLAB Answers — New Questions

​

Hi,
I am trying to simulate a gear pair contact analysis in Simscape where I import the bodies from stl file. Upon simulation, the gear tooth meshings are not happening correctly and I have severe interference. I tried solving the issue with different solvers, but still the meshing is not appropriate. Could you please suggest how I can solve this issue?
Thanks,
AnandHi,
I am trying to simulate a gear pair contact analysis in Simscape where I import the bodies from stl file. Upon simulation, the gear tooth meshings are not happening correctly and I have severe interference. I tried solving the issue with different solvers, but still the meshing is not appropriate. Could you please suggest how I can solve this issue?
Thanks,
Anand Hi,
I am trying to simulate a gear pair contact analysis in Simscape where I import the bodies from stl file. Upon simulation, the gear tooth meshings are not happening correctly and I have severe interference. I tried solving the issue with different solvers, but still the meshing is not appropriate. Could you please suggest how I can solve this issue?
Thanks,
Anand simscape, contact, gears, contact analysis MATLAB Answers — New Questions

​

Dear all,
I am currently trying to create a custom component block for Simscape Thermal Liquid that models the heat transfer behaviour of a specific heat exchanger between two different thermal liquids. The code creates the block with no errors, nor warnings, and runs fine as long as I do not define thermal properties for both liquids. When I do define thermal properties for both liquids, I get the following error:

I imagine that the error comes from the fact that my code "expects" the 4 nodes (in/out for both liquids) to share properties, but I cannot find where that definition comes from…
Does anyone know how to define nodes that do not share fluid properties?

As a simpler test case, I am trying to make it work with a custom component block based on the Flow Rate Sensor (TL) library block, with 4 ports instead of 2. Same error comes up, but the code is much simpler to work with:
component flow_sensor_two_fluids
nodes
A = foundation.thermal_liquid.thermal_liquid; % A :left
B = foundation.thermal_liquid.thermal_liquid; % B :right
C = foundation.thermal_liquid.thermal_liquid; % C :left
D = foundation.thermal_liquid.thermal_liquid; % D :right
end
outputs
M1 = {0, ‘kg/s’};
M2 = {0, ‘kg/s’};
end
annotations
[M1] : Side=top
[M2] : Side=bottom
end
variables (Access = protected, ExternalAccess = none)
mdot1 = {0, ‘kg/s’}; % Mass flow rate from port A to port B
Phi1 = {0, ‘kW’ }; % Energy flow rate from port A to port B
mdot2 = {0, ‘kg/s’}; % Mass flow rate from port C to port D
Phi2 = {0, ‘kW’ }; % Energy flow rate from port C to port D
end
branches
mdot1 : A.mdot -> B.mdot;
Phi1 : A.Phi -> B.Phi;
mdot2 : C.mdot -> D.mdot;
Phi2 : C.Phi -> D.Phi;
end
equations
M1 == mdot1;
A.p == B.p;
A.T == B.T;
M2 == mdot2;
C.p == D.p;
C.T == D.T;
end
end

Thank you for your help!
PS: (I am aware that there already exists a heat exchanger (TL-TL) block that MathWorks provide, but would prefer to create my own)Dear all,
I am currently trying to create a custom component block for Simscape Thermal Liquid that models the heat transfer behaviour of a specific heat exchanger between two different thermal liquids. The code creates the block with no errors, nor warnings, and runs fine as long as I do not define thermal properties for both liquids. When I do define thermal properties for both liquids, I get the following error:

I imagine that the error comes from the fact that my code "expects" the 4 nodes (in/out for both liquids) to share properties, but I cannot find where that definition comes from…
Does anyone know how to define nodes that do not share fluid properties?

As a simpler test case, I am trying to make it work with a custom component block based on the Flow Rate Sensor (TL) library block, with 4 ports instead of 2. Same error comes up, but the code is much simpler to work with:
component flow_sensor_two_fluids
nodes
A = foundation.thermal_liquid.thermal_liquid; % A :left
B = foundation.thermal_liquid.thermal_liquid; % B :right
C = foundation.thermal_liquid.thermal_liquid; % C :left
D = foundation.thermal_liquid.thermal_liquid; % D :right
end
outputs
M1 = {0, ‘kg/s’};
M2 = {0, ‘kg/s’};
end
annotations
[M1] : Side=top
[M2] : Side=bottom
end
variables (Access = protected, ExternalAccess = none)
mdot1 = {0, ‘kg/s’}; % Mass flow rate from port A to port B
Phi1 = {0, ‘kW’ }; % Energy flow rate from port A to port B
mdot2 = {0, ‘kg/s’}; % Mass flow rate from port C to port D
Phi2 = {0, ‘kW’ }; % Energy flow rate from port C to port D
end
branches
mdot1 : A.mdot -> B.mdot;
Phi1 : A.Phi -> B.Phi;
mdot2 : C.mdot -> D.mdot;
Phi2 : C.Phi -> D.Phi;
end
equations
M1 == mdot1;
A.p == B.p;
A.T == B.T;
M2 == mdot2;
C.p == D.p;
C.T == D.T;
end
end

Thank you for your help!
PS: (I am aware that there already exists a heat exchanger (TL-TL) block that MathWorks provide, but would prefer to create my own) Dear all,
I am currently trying to create a custom component block for Simscape Thermal Liquid that models the heat transfer behaviour of a specific heat exchanger between two different thermal liquids. The code creates the block with no errors, nor warnings, and runs fine as long as I do not define thermal properties for both liquids. When I do define thermal properties for both liquids, I get the following error:

I imagine that the error comes from the fact that my code "expects" the 4 nodes (in/out for both liquids) to share properties, but I cannot find where that definition comes from…
Does anyone know how to define nodes that do not share fluid properties?

As a simpler test case, I am trying to make it work with a custom component block based on the Flow Rate Sensor (TL) library block, with 4 ports instead of 2. Same error comes up, but the code is much simpler to work with:
component flow_sensor_two_fluids
nodes
A = foundation.thermal_liquid.thermal_liquid; % A :left
B = foundation.thermal_liquid.thermal_liquid; % B :right
C = foundation.thermal_liquid.thermal_liquid; % C :left
D = foundation.thermal_liquid.thermal_liquid; % D :right
end
outputs
M1 = {0, ‘kg/s’};
M2 = {0, ‘kg/s’};
end
annotations
[M1] : Side=top
[M2] : Side=bottom
end
variables (Access = protected, ExternalAccess = none)
mdot1 = {0, ‘kg/s’}; % Mass flow rate from port A to port B
Phi1 = {0, ‘kW’ }; % Energy flow rate from port A to port B
mdot2 = {0, ‘kg/s’}; % Mass flow rate from port C to port D
Phi2 = {0, ‘kW’ }; % Energy flow rate from port C to port D
end
branches
mdot1 : A.mdot -> B.mdot;
Phi1 : A.Phi -> B.Phi;
mdot2 : C.mdot -> D.mdot;
Phi2 : C.Phi -> D.Phi;
end
equations
M1 == mdot1;
A.p == B.p;
A.T == B.T;
M2 == mdot2;
C.p == D.p;
C.T == D.T;
end
end

Thank you for your help!
PS: (I am aware that there already exists a heat exchanger (TL-TL) block that MathWorks provide, but would prefer to create my own) simscape, custom components, themal liquid MATLAB Answers — New Questions

​

I want to make curve fitting to these points but when i made it the blue straight line appeared. What does it mean ?I want to make curve fitting to these points but when i made it the blue straight line appeared. What does it mean ? I want to make curve fitting to these points but when i made it the blue straight line appeared. What does it mean ? matlab, curve fitting MATLAB Answers — New Questions

​

Hello,
We have Matlab R2023a installed on Oracle Linux8. Below is the message user gets. He reports that he would get a pop up Window that says "Oops Were sorry, it looks like a problem occurred." He says that when this happens matlab doesn’t crash, it marks the beginning of the GUI glitches. MatLab turns all white, And I get a ldd error in the console that spawned matlab, it was related to loading/drawing from what he remembers
We had MATE desktop and that was not working, it was worse with glitches according to the user.

id 6f789c523fa312a7f9199f39a72694e68987d191
reason: traps: MATLABWindow[3569572] general protection fault ip:7f76175fabba sp:7ffe77621cf0 error:0 in libgtk-x11-2.0.so.0.2400.31[7f7617419000+260000]

Can anyone tell me if they have seen this or can assist on how to resolve?
thanks,
DennisHello,
We have Matlab R2023a installed on Oracle Linux8. Below is the message user gets. He reports that he would get a pop up Window that says "Oops Were sorry, it looks like a problem occurred." He says that when this happens matlab doesn’t crash, it marks the beginning of the GUI glitches. MatLab turns all white, And I get a ldd error in the console that spawned matlab, it was related to loading/drawing from what he remembers
We had MATE desktop and that was not working, it was worse with glitches according to the user.

id 6f789c523fa312a7f9199f39a72694e68987d191
reason: traps: MATLABWindow[3569572] general protection fault ip:7f76175fabba sp:7ffe77621cf0 error:0 in libgtk-x11-2.0.so.0.2400.31[7f7617419000+260000]

Can anyone tell me if they have seen this or can assist on how to resolve?
thanks,
Dennis Hello,
We have Matlab R2023a installed on Oracle Linux8. Below is the message user gets. He reports that he would get a pop up Window that says "Oops Were sorry, it looks like a problem occurred." He says that when this happens matlab doesn’t crash, it marks the beginning of the GUI glitches. MatLab turns all white, And I get a ldd error in the console that spawned matlab, it was related to loading/drawing from what he remembers
We had MATE desktop and that was not working, it was worse with glitches according to the user.

id 6f789c523fa312a7f9199f39a72694e68987d191
reason: traps: MATLABWindow[3569572] general protection fault ip:7f76175fabba sp:7ffe77621cf0 error:0 in libgtk-x11-2.0.so.0.2400.31[7f7617419000+260000]

Can anyone tell me if they have seen this or can assist on how to resolve?
thanks,
Dennis general protection fault, ibgtk-x11-2.0.so.0.2400.31 MATLAB Answers — New Questions

​

I am attempting to create a whirl flutter diagram based on these calculations by identifying regions of instability such as flutter and divergence areas by examining the eigenvalues of the system. As my coefficients are periodic
Is my approach for determining the Stiffnesses and angles correct, and how can I change the process using the Floquet technique and the Mathieu equation? Because ultimately, the boundries are not shown correctly according to the reference.
clc;
clear all;

% Define parameters
N = 2; % Number of blades

I_thetaoverI_b = 2; % Moment of inertia pitch axis over I_b
I_psioverI_b = 2; % Moment of inertia yaw axis over I_b

C_thetaoverI_b = 0.00; % Damping coefficient over I_b
C_psioverI_b = 0.00; % Damping coefficient over I_b

h = 0.3; % rotor mast height, wing tip spar to rotor hub
hoverR = 0.34;
R = h / hoverR;

gamma = 4; % lock number

V = 1000; % the rotor forward velocity [knots]
Omega = V/R; % the rotor rotational speed [RPM]

freq_1_over_Omega = 1 / Omega;

%the flap moment aerodynamic coefficients for large V
M_b = -(1/10)*V;
M_u = 1/6;

%the propeller aerodynamic coefficients
H_u = V/2;

% Frequency ranges
f_pitch= 0.001:0.5:5;
f_yaw= 0.001:0.5:5;

% Time periods for pitch and yaw
T_pitch = 1 ./ (2 * pi * f_pitch);
T_yaw = 1 ./ (2 * pi * f_yaw);

divergence_map = [];
Rdivergence_map = [];
unstable = [];

% Modify the loop to iterate over time points
for i = 1:length(T_pitch)
for j = 1:length(T_yaw)

T = max(T_pitch(i), T_yaw(j)); % Use the maximum period to cover all dynamics
t_steps = linspace(0, T, 100); % Time steps within one period

for t = t_steps
% Angular frequencies for the current time point
w_omega_pitch = 2 * pi / T_pitch(i);
w_omega_yaw = 2 * pi / T_yaw(j);

K_psi = (w_omega_pitch^2) * I_psioverI_b;
K_theta = (w_omega_yaw^2) * I_thetaoverI_b;

% Calculate matrices at time t using harmonic motion expressions
phi = 2 * pi * t / T; % Phase variation over the period

% Define inertia matrix [M]
M_matrix = [I_thetaoverI_b + 1 + cos(2*phi), -sin(2*phi);
-sin(2*phi), I_psioverI_b + 1 – cos(2*phi)];

% Define damping matrix [D]
D11 = h^2*gamma*H_u*(1 – cos(2*phi)) – gamma*M_b*(1 + cos(2*phi)) – (2 + 2*h*gamma*M_u)*sin(2*phi);
D12 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) – 2*(1 + cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D21 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) + 2*(1 – cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D22 = h^2*gamma*H_u*(1 + cos(2*phi)) – gamma*M_b*(1 – cos(2*phi)) + (2 + 2*h*gamma*M_u)*sin(2*phi);

D_matrix = [D11, D12;
D21, D22];

% Define stiffness matrix [K]
K11 = K_theta – h*gamma*V*H_u*(1 – cos(2*phi)) + gamma*V*M_u*sin(2*phi);
K12 = -h*V*gamma*H_u*sin(2*phi) + gamma*V*M_u*(1 + cos(2*phi));
K21 = -h*gamma*V*H_u*sin(2*phi) – gamma*V*M_u*(1 – cos(2*phi));
K22 = K_psi – h*gamma*V*H_u*(1 + cos(2*phi)) – gamma*V*M_u*sin(2*phi);

K_matrix = [K11, K12;
K21, K22];

% Compute the system matrices

M11 = M_matrix(1, 1); M12 = M_matrix(1, 2); M21 = M_matrix(2, 1); M22 = M_matrix(2, 2);
D11 = D_matrix(1, 1); D12 = D_matrix(1, 2); D21 = D_matrix(2, 1); D22 = D_matrix(2, 2);
K11 = K_matrix(1, 1); K12 = K_matrix(1, 2); K21 = K_matrix(2, 1); K22 = K_matrix(2, 2);

P0 = M11*M22-M12*M21;
P1 = (- D11*M22*1j – D22*M11*1j + M12*D21*j + D12*M21*j);
P2 = (D11*D22*(1j)^2 – K22*M11 – K11*M22 – D12*D21*(1j)^2 + M12*K21 + M21*K12);
P3 = (D11*K22*1j – D12*K21*1j – D21*K12*1j + D22*K11*1j);
P4 = K11*K22 – K12*K21;

P = roots([P0, P1, P2, P3, P4]);

r = 1 * P;

%Flutter
for k = 1:length(r)

if (real(r(k)) > 0)
if (imag(r(k)) <= 0)
unstable = [unstable; phi, K_psi, K_theta];

% Proximity check for 1/Ω divergence
if abs(real(r(k)) – freq_1_over_Omega) < 1e-5
Rdivergence_map = [Rdivergence_map; phi, K_psi, K_theta];

end
end
end

end

%Divergence

if (real(det(K_matrix)) < 0)
divergence_map = [divergence_map; t, K_psi, K_theta];
end

end
end
end

% Plotting section

figure;
hold on;

scatter(unstable(:,2), unstable(:,3), ‘filled’);
scatter(divergence_map(:,2), divergence_map(:,3), ‘filled’, ‘r’);
scatter(Rdivergence_map(:,2), Rdivergence_map(:,3), ‘filled’, ‘g’);

xlabel(‘K_psi’);
ylabel(‘K_theta’);

title(‘Whirl Flutter Diagram’);
legend(‘Flutter area’, ‘Divergence area’, ‘1/Ω Divergence area’);

hold off;I am attempting to create a whirl flutter diagram based on these calculations by identifying regions of instability such as flutter and divergence areas by examining the eigenvalues of the system. As my coefficients are periodic
Is my approach for determining the Stiffnesses and angles correct, and how can I change the process using the Floquet technique and the Mathieu equation? Because ultimately, the boundries are not shown correctly according to the reference.
clc;
clear all;

% Define parameters
N = 2; % Number of blades

I_thetaoverI_b = 2; % Moment of inertia pitch axis over I_b
I_psioverI_b = 2; % Moment of inertia yaw axis over I_b

C_thetaoverI_b = 0.00; % Damping coefficient over I_b
C_psioverI_b = 0.00; % Damping coefficient over I_b

h = 0.3; % rotor mast height, wing tip spar to rotor hub
hoverR = 0.34;
R = h / hoverR;

gamma = 4; % lock number

V = 1000; % the rotor forward velocity [knots]
Omega = V/R; % the rotor rotational speed [RPM]

freq_1_over_Omega = 1 / Omega;

%the flap moment aerodynamic coefficients for large V
M_b = -(1/10)*V;
M_u = 1/6;

%the propeller aerodynamic coefficients
H_u = V/2;

% Frequency ranges
f_pitch= 0.001:0.5:5;
f_yaw= 0.001:0.5:5;

% Time periods for pitch and yaw
T_pitch = 1 ./ (2 * pi * f_pitch);
T_yaw = 1 ./ (2 * pi * f_yaw);

divergence_map = [];
Rdivergence_map = [];
unstable = [];

% Modify the loop to iterate over time points
for i = 1:length(T_pitch)
for j = 1:length(T_yaw)

T = max(T_pitch(i), T_yaw(j)); % Use the maximum period to cover all dynamics
t_steps = linspace(0, T, 100); % Time steps within one period

for t = t_steps
% Angular frequencies for the current time point
w_omega_pitch = 2 * pi / T_pitch(i);
w_omega_yaw = 2 * pi / T_yaw(j);

K_psi = (w_omega_pitch^2) * I_psioverI_b;
K_theta = (w_omega_yaw^2) * I_thetaoverI_b;

% Calculate matrices at time t using harmonic motion expressions
phi = 2 * pi * t / T; % Phase variation over the period

% Define inertia matrix [M]
M_matrix = [I_thetaoverI_b + 1 + cos(2*phi), -sin(2*phi);
-sin(2*phi), I_psioverI_b + 1 – cos(2*phi)];

% Define damping matrix [D]
D11 = h^2*gamma*H_u*(1 – cos(2*phi)) – gamma*M_b*(1 + cos(2*phi)) – (2 + 2*h*gamma*M_u)*sin(2*phi);
D12 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) – 2*(1 + cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D21 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) + 2*(1 – cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D22 = h^2*gamma*H_u*(1 + cos(2*phi)) – gamma*M_b*(1 – cos(2*phi)) + (2 + 2*h*gamma*M_u)*sin(2*phi);

D_matrix = [D11, D12;
D21, D22];

% Define stiffness matrix [K]
K11 = K_theta – h*gamma*V*H_u*(1 – cos(2*phi)) + gamma*V*M_u*sin(2*phi);
K12 = -h*V*gamma*H_u*sin(2*phi) + gamma*V*M_u*(1 + cos(2*phi));
K21 = -h*gamma*V*H_u*sin(2*phi) – gamma*V*M_u*(1 – cos(2*phi));
K22 = K_psi – h*gamma*V*H_u*(1 + cos(2*phi)) – gamma*V*M_u*sin(2*phi);

K_matrix = [K11, K12;
K21, K22];

% Compute the system matrices

M11 = M_matrix(1, 1); M12 = M_matrix(1, 2); M21 = M_matrix(2, 1); M22 = M_matrix(2, 2);
D11 = D_matrix(1, 1); D12 = D_matrix(1, 2); D21 = D_matrix(2, 1); D22 = D_matrix(2, 2);
K11 = K_matrix(1, 1); K12 = K_matrix(1, 2); K21 = K_matrix(2, 1); K22 = K_matrix(2, 2);

P0 = M11*M22-M12*M21;
P1 = (- D11*M22*1j – D22*M11*1j + M12*D21*j + D12*M21*j);
P2 = (D11*D22*(1j)^2 – K22*M11 – K11*M22 – D12*D21*(1j)^2 + M12*K21 + M21*K12);
P3 = (D11*K22*1j – D12*K21*1j – D21*K12*1j + D22*K11*1j);
P4 = K11*K22 – K12*K21;

P = roots([P0, P1, P2, P3, P4]);

r = 1 * P;

%Flutter
for k = 1:length(r)

if (real(r(k)) > 0)
if (imag(r(k)) <= 0)
unstable = [unstable; phi, K_psi, K_theta];

% Proximity check for 1/Ω divergence
if abs(real(r(k)) – freq_1_over_Omega) < 1e-5
Rdivergence_map = [Rdivergence_map; phi, K_psi, K_theta];

end
end
end

end

%Divergence

if (real(det(K_matrix)) < 0)
divergence_map = [divergence_map; t, K_psi, K_theta];
end

end
end
end

% Plotting section

figure;
hold on;

scatter(unstable(:,2), unstable(:,3), ‘filled’);
scatter(divergence_map(:,2), divergence_map(:,3), ‘filled’, ‘r’);
scatter(Rdivergence_map(:,2), Rdivergence_map(:,3), ‘filled’, ‘g’);

xlabel(‘K_psi’);
ylabel(‘K_theta’);

title(‘Whirl Flutter Diagram’);
legend(‘Flutter area’, ‘Divergence area’, ‘1/Ω Divergence area’);

hold off; I am attempting to create a whirl flutter diagram based on these calculations by identifying regions of instability such as flutter and divergence areas by examining the eigenvalues of the system. As my coefficients are periodic
Is my approach for determining the Stiffnesses and angles correct, and how can I change the process using the Floquet technique and the Mathieu equation? Because ultimately, the boundries are not shown correctly according to the reference.
clc;
clear all;

% Define parameters
N = 2; % Number of blades

I_thetaoverI_b = 2; % Moment of inertia pitch axis over I_b
I_psioverI_b = 2; % Moment of inertia yaw axis over I_b

C_thetaoverI_b = 0.00; % Damping coefficient over I_b
C_psioverI_b = 0.00; % Damping coefficient over I_b

h = 0.3; % rotor mast height, wing tip spar to rotor hub
hoverR = 0.34;
R = h / hoverR;

gamma = 4; % lock number

V = 1000; % the rotor forward velocity [knots]
Omega = V/R; % the rotor rotational speed [RPM]

freq_1_over_Omega = 1 / Omega;

%the flap moment aerodynamic coefficients for large V
M_b = -(1/10)*V;
M_u = 1/6;

%the propeller aerodynamic coefficients
H_u = V/2;

% Frequency ranges
f_pitch= 0.001:0.5:5;
f_yaw= 0.001:0.5:5;

% Time periods for pitch and yaw
T_pitch = 1 ./ (2 * pi * f_pitch);
T_yaw = 1 ./ (2 * pi * f_yaw);

divergence_map = [];
Rdivergence_map = [];
unstable = [];

% Modify the loop to iterate over time points
for i = 1:length(T_pitch)
for j = 1:length(T_yaw)

T = max(T_pitch(i), T_yaw(j)); % Use the maximum period to cover all dynamics
t_steps = linspace(0, T, 100); % Time steps within one period

for t = t_steps
% Angular frequencies for the current time point
w_omega_pitch = 2 * pi / T_pitch(i);
w_omega_yaw = 2 * pi / T_yaw(j);

K_psi = (w_omega_pitch^2) * I_psioverI_b;
K_theta = (w_omega_yaw^2) * I_thetaoverI_b;

% Calculate matrices at time t using harmonic motion expressions
phi = 2 * pi * t / T; % Phase variation over the period

% Define inertia matrix [M]
M_matrix = [I_thetaoverI_b + 1 + cos(2*phi), -sin(2*phi);
-sin(2*phi), I_psioverI_b + 1 – cos(2*phi)];

% Define damping matrix [D]
D11 = h^2*gamma*H_u*(1 – cos(2*phi)) – gamma*M_b*(1 + cos(2*phi)) – (2 + 2*h*gamma*M_u)*sin(2*phi);
D12 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) – 2*(1 + cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D21 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) + 2*(1 – cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D22 = h^2*gamma*H_u*(1 + cos(2*phi)) – gamma*M_b*(1 – cos(2*phi)) + (2 + 2*h*gamma*M_u)*sin(2*phi);

D_matrix = [D11, D12;
D21, D22];

% Define stiffness matrix [K]
K11 = K_theta – h*gamma*V*H_u*(1 – cos(2*phi)) + gamma*V*M_u*sin(2*phi);
K12 = -h*V*gamma*H_u*sin(2*phi) + gamma*V*M_u*(1 + cos(2*phi));
K21 = -h*gamma*V*H_u*sin(2*phi) – gamma*V*M_u*(1 – cos(2*phi));
K22 = K_psi – h*gamma*V*H_u*(1 + cos(2*phi)) – gamma*V*M_u*sin(2*phi);

K_matrix = [K11, K12;
K21, K22];

% Compute the system matrices

M11 = M_matrix(1, 1); M12 = M_matrix(1, 2); M21 = M_matrix(2, 1); M22 = M_matrix(2, 2);
D11 = D_matrix(1, 1); D12 = D_matrix(1, 2); D21 = D_matrix(2, 1); D22 = D_matrix(2, 2);
K11 = K_matrix(1, 1); K12 = K_matrix(1, 2); K21 = K_matrix(2, 1); K22 = K_matrix(2, 2);

P0 = M11*M22-M12*M21;
P1 = (- D11*M22*1j – D22*M11*1j + M12*D21*j + D12*M21*j);
P2 = (D11*D22*(1j)^2 – K22*M11 – K11*M22 – D12*D21*(1j)^2 + M12*K21 + M21*K12);
P3 = (D11*K22*1j – D12*K21*1j – D21*K12*1j + D22*K11*1j);
P4 = K11*K22 – K12*K21;

P = roots([P0, P1, P2, P3, P4]);

r = 1 * P;

%Flutter
for k = 1:length(r)

if (real(r(k)) > 0)
if (imag(r(k)) <= 0)
unstable = [unstable; phi, K_psi, K_theta];

% Proximity check for 1/Ω divergence
if abs(real(r(k)) – freq_1_over_Omega) < 1e-5
Rdivergence_map = [Rdivergence_map; phi, K_psi, K_theta];

end
end
end

end

%Divergence

if (real(det(K_matrix)) < 0)
divergence_map = [divergence_map; t, K_psi, K_theta];
end

end
end
end

% Plotting section

figure;
hold on;

scatter(unstable(:,2), unstable(:,3), ‘filled’);
scatter(divergence_map(:,2), divergence_map(:,3), ‘filled’, ‘r’);
scatter(Rdivergence_map(:,2), Rdivergence_map(:,3), ‘filled’, ‘g’);

xlabel(‘K_psi’);
ylabel(‘K_theta’);

title(‘Whirl Flutter Diagram’);
legend(‘Flutter area’, ‘Divergence area’, ‘1/Ω Divergence area’);

hold off; floquet technic, dynamical system MATLAB Answers — New Questions

​

Hi Everyone,
I am currently working with a very long equation. And when I output it in the livescript, MATLAB finds several sigmas (see screenshot). I would like to have this equation with the sigmas in order to process it in another function.
So far I have tried [r,sigma] = subexpr(expr). I cancelled this command after more than 1 hour of calculation. In addition, subexpr, if I have understood it correctly, only looks for one sigma.
I hope someone here can help me.

I am working with Matla 2017b and the symbolic toolboxHi Everyone,
I am currently working with a very long equation. And when I output it in the livescript, MATLAB finds several sigmas (see screenshot). I would like to have this equation with the sigmas in order to process it in another function.
So far I have tried [r,sigma] = subexpr(expr). I cancelled this command after more than 1 hour of calculation. In addition, subexpr, if I have understood it correctly, only looks for one sigma.
I hope someone here can help me.

I am working with Matla 2017b and the symbolic toolbox Hi Everyone,
I am currently working with a very long equation. And when I output it in the livescript, MATLAB finds several sigmas (see screenshot). I would like to have this equation with the sigmas in order to process it in another function.
So far I have tried [r,sigma] = subexpr(expr). I cancelled this command after more than 1 hour of calculation. In addition, subexpr, if I have understood it correctly, only looks for one sigma.
I hope someone here can help me.

I am working with Matla 2017b and the symbolic toolbox subexpr, matlab, simplify MATLAB Answers — New Questions

​

I am working on simulating heat transfer in a component that consists of multiple solid layers and an enclosed air cavity using the PDE Toolbox in MATLAB. My goal is to account for heat transfer mechanisms such as radiation and convection between the air in the cavity and the surrounding solid layers. is this possible with the pde toolbox? Is there a solutuion without modelling the air as a solid material?I am working on simulating heat transfer in a component that consists of multiple solid layers and an enclosed air cavity using the PDE Toolbox in MATLAB. My goal is to account for heat transfer mechanisms such as radiation and convection between the air in the cavity and the surrounding solid layers. is this possible with the pde toolbox? Is there a solutuion without modelling the air as a solid material? I am working on simulating heat transfer in a component that consists of multiple solid layers and an enclosed air cavity using the PDE Toolbox in MATLAB. My goal is to account for heat transfer mechanisms such as radiation and convection between the air in the cavity and the surrounding solid layers. is this possible with the pde toolbox? Is there a solutuion without modelling the air as a solid material? heat transfer, air cavity, pde MATLAB Answers — New Questions

​

Hi, I have been running a matlab script on a daily basis using windows task scheduler for the past few weeks and have noticed that the output image plots appear compressed (the arrows and contours are squished together, implying some sort of scale issue(?)) when compared with running the same script with matlab already running on my desktop. My script does specify the dimensions of the figure, but these seem to be ignored. Is there a way to correct for this? Related, if I can resolve the former issues, is there a way to force Task Scheduler to run matlab so that it is maximised (not behind the scene).
I’m using the following in Task scheduler to initiate my script:
matlab -r "cd(‘C:MatlabScripts’); run scriptname.m; pause(10)"
Thank you for any thoughts on this,
JonHi, I have been running a matlab script on a daily basis using windows task scheduler for the past few weeks and have noticed that the output image plots appear compressed (the arrows and contours are squished together, implying some sort of scale issue(?)) when compared with running the same script with matlab already running on my desktop. My script does specify the dimensions of the figure, but these seem to be ignored. Is there a way to correct for this? Related, if I can resolve the former issues, is there a way to force Task Scheduler to run matlab so that it is maximised (not behind the scene).
I’m using the following in Task scheduler to initiate my script:
matlab -r "cd(‘C:MatlabScripts’); run scriptname.m; pause(10)"
Thank you for any thoughts on this,
Jon Hi, I have been running a matlab script on a daily basis using windows task scheduler for the past few weeks and have noticed that the output image plots appear compressed (the arrows and contours are squished together, implying some sort of scale issue(?)) when compared with running the same script with matlab already running on my desktop. My script does specify the dimensions of the figure, but these seem to be ignored. Is there a way to correct for this? Related, if I can resolve the former issues, is there a way to force Task Scheduler to run matlab so that it is maximised (not behind the scene).
I’m using the following in Task scheduler to initiate my script:
matlab -r "cd(‘C:MatlabScripts’); run scriptname.m; pause(10)"
Thank you for any thoughts on this,
Jon automatically run script problem with plots MATLAB Answers — New Questions

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