How do i add a function that needs inputs to the main code? (Nonlinear pendulum code)

Hi guys,

I have the following two functions, pend_l and pend_n and the script file pend_solve.

the functions contain a variable "wsq" which needs to accept input values of L,M, b, so that the resulting value of wsq is substituted in the equations in

pend_l and pend_n.

I have been able to find the value of wsq as a seperate function, but i need to consolidate it with the rest of the code.

I do not know if i should add the expansion of wsq to the functions or to the script file, so that the output, with the plots and all, takes the value of wsq into consideration, after i input the values of L, M, and b.

Below is how i find the value of wsq seperately

function wsq = findwsq 

prompt1 = 'Enter value of L';
prompt2 = 'Enter value of M';
prompt3 = 'Enter value of b';
L = input(prompt1)
M = input(prompt2)
b = input(prompt3)
wsq = (12*9.81*L)/((4*(L.^2))+(b.^2)-(12*L*M)+(12*(M.^2))); 
disp(wsq)
end 

My function files are:

pend_l

function xdot = pend_l(t1,x)
wsq=3.5;         %i need to replace the constant value (arbitrarily taken as 3.5) of wsq with the above function 
xdot = [x(2); -wsq*x(1)];

i need to replace the above wsq value with the function wsq such that pend_l computes xdot using the inputted values of L, M, b

similarly, i have

pend_n

function ydot = pend_n(t2,y)
wsq=3.5;         % same value of wsq in both cases is required
ydot = [y(2); -wsq*sin(y(1))];

and my script file,

pend_solve

clear all;
clc;
clf;
tic;
tspan = 0:0.01:10;
a=pi/2;
b=0;
x0 = [a; b];
[t1,x] = ode45(@pend_l,tspan,x0);
X1 = x(:,1);
X2 = x(:,2);

y0 = [a ; b];
[t2,y] = ode45(@pend_n,tspan,y0);
Y1 = y(:,1);
Y2 = y(:,2);
figure(1);
subplot(2,2,1);
plot(t1,X1); 
xlabel('Time (s)');
ylabel('Displacement (rad)');
hold on;
grid on;
plot(t2,Y1);
% legend('Linear','Non Linear');
subplot(2,2,2);
% figure(2);
plot(t1,X2);
xlabel('Time (s)');
ylabel('Velocity (rad/s)');

hold on;
grid on;
plot(t2,Y2);
subplot(2,2,3);
plot(X1,X2);
hold on;
plot(Y1,Y2);
xlabel('Displacement (rad)');
ylabel('Velocity (rad/s)');

grid on;

toc;

upon executing pend_solve with fixed value of wsq (without using the function wsq), i get three plots.

How do i make it so that the function wsq becomes a part of the main code such that the plots are plotted upon taking the computed value of wsq into consideration?

Answer 1

[Moses Huang]

To integrate wsq into your main code, you can do the following:

1. Update the definition of pend_l and pend_n to take the wsq parameter:

function xdot = pend_l(t1,x,wsq)
    xdot = [x(2); -wsq*x(1)];
end

function ydot = pend_n(t2,y,wsq)
    ydot = [y(2); -wsq*sin(y(1))];
end

2. Update pend_solve to pass in wsq. Since ode45 only take function handles that accept two inputs, we have to define an anonymous function that calls pend_l and pend_n and pass in wsq to them. Relevant MATLAB documentation can be found here. Below I'm reproducing only a portion of your code and modified it:

wsq = 3.5; %Replace this with a call to findwsq function
[t1,x] = ode45(@(t,y) pend_l(t,y,wsq),tspan,x0);
...
[t2,y] = ode45(@(t,y) pend_n(t,y,wsq),tspan,y0);
...

3. Now you can use findwsq function to set wsq according to user input

[KLETECH MOTORSPORTS]

I'm sorry, but point 2 is not very clear to me. Could you please elaborate more simply?

Also, why

[t1,x] = ode45(@(t,y) pend_l(t,y,wsq),tspan,x0);

does this function have (t,y) in the bracket instead of (t,x)?

Answer 2

[KLETECH MOTORSPORTS]

i tried modifying it the way you explained but i think i have made a mistake somewhere:

pend_l

function xdot = pend_l(t1,x,wsq)
xdot = [x(2); -wsq*x(1)];
end

pend_n

function ydot = pend_n(t2,y,wsq)
ydot = [y(2); -wsq*sin(y(1))];
end

findwsq

function wsq = findwsq(L,b,M)

prompt1 = 'Enter value of L';
prompt2 = 'Enter value of M';
prompt3 = 'Enter value of b';
L = input(prompt1)
M = input(prompt2)
b = input(prompt3)
wsq = (12*9.81*L)/((4*(L.^2))+(b.^2)-(12*L*M)+(12*(M.^2))); 
disp(wsq)
end

pend_solve

clc;
clf;
tic;
tspan = 0:0.01:10;
a=pi/2;
b=0;
x0 = [a; b];
findwsq(wsq)  %callinf findwsq here
[t1,x] = ode45(@(t1,x) pend_l(t1,x,wsq),tspan,x0);
X1 = x(:,1);
X2 = x(:,2);

y0 = [a ; b];
findwsq(wsq)  %caling findwsq here
[t2,y] = ode45(@(t2,y) pend_n(t2,y,wsq),tspan,y0);
Y1 = y(:,1);
Y2 = y(:,2);
figure(1);
subplot(2,2,1);
 plot(t1,X1); 
xlabel('Time (s)');
ylabel('Displacement (rad)');
hold on;
grid on;
plot(t2,Y1);
legend('Linear','Non Linear');
subplot(2,2,2);
% figure(2);
plot(t1,X2);
xlabel('Time (s)');
ylabel('Velocity (rad/s)');

hold on;
grid on;
plot(t2,Y2);
subplot(2,2,3);
plot(X1,X2);
hold on;
plot(Y1,Y2);
xlabel('Displacement (rad)');
ylabel('Velocity (rad/s)');

grid on;

toc;

didn't know how to call an anonymous function, but i tried writing this:

i'm positive this is wrong but i didn't know what else to do

function anon = manyinput(pend_l,pend_n,findwsq)

end

[Moses Huang]

I see two issues. 1) Because you are prompting the user to enter L, M and b, you don't need to include them as inputs to findwsq:

function wsq = findwsq()
    prompt1 = 'Enter value of L';
    prompt2 = 'Enter value of M';
    prompt3 = 'Enter value of b';
    L = input(prompt1)
    M = input(prompt2)
    b = input(prompt3)
    wsq = (12*9.81*L)/((4*(L.^2))+(b.^2)-(12*L*M)+(12*(M.^2))); 
    disp(wsq)
end

2) In pend_solve, you need to call findwsq() and assign it to wsq, which will be passed to pend_l and pend_n

clc;
clf;
tic;
tspan = 0:0.01:10;
a=pi/2;
b=0;
x0 = [a; b];
wsq = findwsq(); 
[t1,x] = ode45(@(t1,x) pend_l(t1,x,wsq),tspan,x0);
X1 = x(:,1);
X2 = x(:,2);
y0 = [a ; b];
[t2,y] = ode45(@(t2,y) pend_n(t2,y,wsq),tspan,y0);
Y1 = y(:,1);
Y2 = y(:,2);
figure(1);
subplot(2,2,1);
 plot(t1,X1); 
xlabel('Time (s)');
ylabel('Displacement (rad)');
hold on;
grid on;
plot(t2,Y1);
legend('Linear','Non Linear');
subplot(2,2,2);
% figure(2);
plot(t1,X2);
xlabel('Time (s)');
ylabel('Velocity (rad/s)');
hold on;
grid on;
plot(t2,Y2);
subplot(2,2,3);
plot(X1,X2);
hold on;
plot(Y1,Y2);
xlabel('Displacement (rad)');
ylabel('Velocity (rad/s)');
grid on;
toc;

[KLETECH MOTORSPORTS]

Thank you Moses, i have made the necessary changes and it's working fine.