Rewrite from Mathematica to MATLAB

SO, I have this problem, which I solved for dynamics, but now I should write a code and then generate two plots. (5.38)

I found a solution in Mathematica software, but I can't figure out what am I doing wrong in MATLAB. Here's my code:

% Given
syms theta;
W_A=100;
m_A=W_A/32.2;
W_B=20;
m_B=W_B/32.2;
L=15;
theta_0= deg2rad(70);

% Solve the system of three equations
one = str2sym('W_A*L*(cos(theta)-cos(theta_0))-1/2*m_A*V_A^2-1/2*m_B*V_Bx^2+W_A*L');
two = str2sym('m_B*V_Bx+m_A*(V_Bx+L*theta_1*cos(theta))');
three = str2sym('-V_A^2+(V_Bx+ L*theta_1*cos(theta))^2+(L*theta_1*sin(theta))^2');

[theta_1,V_A,V_Bx] = solve(one,two,three);


% Plot the velocity of the trolley and the speed of the rider as a function of the angle θ of the first half of a full swing
fplot(V_Bx, [-70,70], 'Linewidth',2)
hold on
fplot(V_A, [-70,70], '-.*c')
hold off

% Plot the velocity of the trolley and the speed of the rider as a function of the angle θ of the second half of a full swing
fplot(V_Bx, [-70,70], 'Linewidth',2)
hold on
fplot(V_A, [-70,70], '-.*c')
hold off

Thank you so much in advance!!!

Answer 1

[Ameer Hamza]

Following shows how to write this in MATLAB.

syms theta theta_1 V_A V_Bx;
W_A=100;
m_A=W_A/32.2;
W_B=20;
m_B=W_B/32.2;
L=15;
theta_0= deg2rad(70);
% Solve the system of three equations
one = W_A*L*(cos(theta)-cos(theta_0))-1/2*m_A*V_A^2-1/2*m_B*V_Bx^2+W_A*L;
two = m_B*V_Bx+m_A*(V_Bx+L*theta_1*cos(theta));
three = -V_A^2+(V_Bx+ L*theta_1*cos(theta))^2+(L*theta_1*sin(theta))^2;
[theta_1,V_A,V_Bx] = solve(one,two,three);
% Plot the velocity of the trolley and the speed of the rider as a function of the angle θ of the first half of a full swing
fplot(V_Bx, [-70,70], 'Linewidth',2)
hold on
fplot(V_A, [-70,70], '-.*c')
hold off
% Plot the velocity of the trolley and the speed of the rider as a function of the angle θ of the second half of a full swing
fplot(V_Bx, [-70,70], 'Linewidth',2)
hold on
fplot(V_A, [-70,70], '-.*c')
hold off

The above can take a long time to plot because there are 12 solutions given by solve() functions. To speed up the computation, you can convert the functions to numeric function handle using matlabFunction() and then use fplot().

[Kseniia Kudriavtceva]

But you did nothing to my code.

Just copied. Why do you do so?

I can't put numeric function, because I don't have it.

[Walter Roberson]

Your code used str2sym

[Walter Roberson]

When you use str2sym then there is no connection made between variables you mention and variables that you set at the MATLAB level with the same name.

A=1
eqn = str2sym('A')

eqn will not be a symbolic 1, it will be a reference to a symbolic variable named A that lives inside the symbolic engine.

You can get a numeric function by using

matlabFunction(V_Bx)

[Kseniia Kudriavtceva]

There's unrecognized function or variable 'theta'

[Kseniia Kudriavtceva]

And here's the graph which I'm getting when put thets as variable in the beggining after syms

[Ameer Hamza]

Yes, there was a theta missing in the first line. I have updated the answer. This graph is likely according to your equations.

[Kseniia Kudriavtceva]

Nope, here's what I should get as a result